MaplePrimes Questions

... to solve familiar problems using Maple. The attached exercises "test" and "test1" don't produce the familiar result. What am I doing wrong?

test.mw

test1.mw

The following Array does not convert to a column vector as described in ?convert,Vector

A := Array([1, 2, 3]);
convert(A, Vector);# the default orientation should be column;
whattype(%);
convert(convert(A, list), Vector);# here the default orientation is column
                         A := [1, 2, 3]

                           [1, 2, 3]

                          Vector[row]

                              [1]
                              [ ]
                              [2]
                              [ ]
                              [3]

Is there something special with the data structure Array that convert(A, Vector[column]) has to be used to convert to a column vector?

Dear All,

I am facing some problems. This kind of error has been shown ""Error, (in plot/iplot2d/expression) bad range arguments 0.3e-1 = .1 .. .5, 0.3e-1 = .1 .. .5"

Error.mw

Hello,

With the new version 2025, double-clicking a file opens a second instance of Maple.

How can I make this open a new tab in the active instance, as it did with version 2024?

Thank you.

Bests regards.

I wanted to try this simplification in Maple 2025, only to find timelimit hangs.

Waited 3 hrs when timelimit was 30 second. It seems simplify got locked up and timelimit does not work.

Not only that, Maple itself hangs and clicking on retsrat kernel or red small bottom at lower level corner in Maple 2025 has no effect at all.  

Only way is to kill all of Maple from command line.

Make sure to save all your work before trying.

There are two bugs here: First is that timelimit still hangs (even though Maplesoft claimed it is fixed almost 5 years ago)

https://www.mapleprimes.com/maplesoftblog/213986-Introducing-Maple-Learn-officially

You will also be pleased to know that Maple 2021 addresses the timelimit() issue that you mentioned.

The second issue is that one can not close the kernel from frontend. (well, this is because kernel hanged)

Note that closing Maple works using File->EXIT but this leaves the Maple kernel/mserver  running  in background!

So had to go kill that process from command line manually also.

So make sure to do this, else you will end up with many mserver processes running in background after maple is closed if you try this more than one time.

Any one knows why this happens for this example? Should not timelimit have finally been fixed in Maple 2025?

I have been complaining about timelimit not always working for ages. Have no idea why Maplesoft can't figure solution to this problem for good. 

timelimit is the most important command for me, as without it, my program will never work and will just keep hanging.

I spend 50% of my time finding worarounds around Maple bugs instead of what I should be doing which is write more code.

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1869. The version installed in this computer is 1866 created 2025, May 6, 10:52 hours Pacific Time, found in the directory /home/me/maple/toolbox/2025/Physics Updates/lib/`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 17 and is the same as the version installed in this computer, created May 5, 2025, 12:37 hours Eastern Time.`

restart;

e:= -a*(-1/2*((1/2*x)^a)^4*(2^a)^4*_C8^4*a*x+1/2*((1/2*x)^a)^3*(2^a)^3*(((2^a)^2*((
1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8^3*x+1/4
*((1/2*x)^a)^2*(2^a)^2*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1
/2*x)^a)^2/_C8^2)^(1/2)*4^(1/2)*(x^2*(((1/2*x)^a)^4*(2^a)^4*_C8^4*a^2+(2^a)^4*(
(1/2*x)^a)^4*_C8^4+2*((1/2*x)^a)^2*(2^a)^2*_C8^2*a^4*b^2-2*((1/2*x)^a)^3*(2^a)^
3*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/
2)*_C8^3*a-4*a^2*b^2*(2^a)^2*((1/2*x)^a)^2*_C8^2+a^6*b^4-2*(1/2*x)^a*2^a*(((2^a
)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a
^3*b^2+2*b^2*(2^a)^2*((1/2*x)^a)^2*_C8^2-a^4*b^4+2*(1/2*x)^a*2^a*(((2^a)^2*((1/
2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a*b^2-a^2
*b^4+b^4)/(a-1)^2/(1+a)^2/_C8^2/((1/2*x)^a)^2/(2^a)^2)^(1/2)*_C8^2*a^2+1/2*a^5*
b^4*x-1/2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((
1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a^2*b^2*x-1/4*((1/2*x)^a)^2*(2^a)^2*(((2^a)^2*((1/
2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*4^(1/2)*(x^2*
(((1/2*x)^a)^4*(2^a)^4*_C8^4*a^2+(2^a)^4*((1/2*x)^a)^4*_C8^4+2*((1/2*x)^a)^2*(2
^a)^2*_C8^2*a^4*b^2-2*((1/2*x)^a)^3*(2^a)^3*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b
^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8^3*a-4*a^2*b^2*(2^a)^2*((1/2*x)
^a)^2*_C8^2+a^6*b^4-2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^
2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a^3*b^2+2*b^2*(2^a)^2*((1/2*x)^a)^2*
_C8^2-a^4*b^4+2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a
)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a*b^2-a^2*b^4+b^4)/(a-1)^2/(1+a)^2/_C8^2/((1
/2*x)^a)^2/(2^a)^2)^(1/2)*_C8^2-a^3*b^4*x+1/2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^
a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*b^2*x+1/2*a*b^
4*x)/(a-1)/(1+a)/_C8^2/(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1
/2*x)^a)^2/_C8^2)^(1/2)/((1/2*x)^a)^2/(2^a)^2:

try
  timelimit(30, (simplify(e) assuming real)):
catch:
   print("cought timelimit");
end try:

 

 

Download timelimit_hang_in_maple_2025.mw

Hello,
Can you tell me how to decompose a rational fraction into simple elements in Fp?

Thank you.

I'm using an old old version of Maple (Maple 7) and there's a mistake in the Mellin Transform which hopefully has long since been fixed in subsequent versions but just in case it hasn't....

I was taking the Mellin Transform of Bessel Functions, specifically BesselK, and it's fine for BesselK(0,x), but when I compute BesselK(0,x^{1/2}), it gives the wrong answer.

In the transform of BesselK(0,x^(1/2)), It should be Gamma(p) not Gamma(p/2).

I'm not sure if this is fixed in newer Maples or if there's a work around. 

Whenever I size a 3d plot, that I'm trying to stretch out the width while keeping the height, never seems to work.  For example using the size=[3000,800] produces a plot area that's bigger but NOT actually a plot stretched in the x axis.  Going to size=[3000,3000] of course then makes the plot and the area bigger and so scales both x and y bigger.  However I don't want the y axis scaled up - I'm trying to scale the plot up - not the area.  And what happened to the window zoom, icon - we've lost zoom control to just magnify + and magnify - (at least in 2022) this seems like a regression. 

Is this plot size a bug or just a plot command that fails to function like it should? 

Hi, I'm new to Maple.

when nesting some multiplications in a summation operator, I get results that I can't figure out.

I've entered 4 formulas that should give the same result, if I understood things correctly. The formula FB gives me problems; am I doing something wrong, or is there a bug in Maple? The problem arose in a more complicated formula, but I trimmed the formula down to a minimum, in order to illustrate the discrepancy.

I hope someone can shed some light on this, because I'm stuck.

Is this a bug (the correct answer = 2)?

 

restart

 

FA := modp(5, product(2, t = 0 .. modp(1-1, 3)))+modp(5, product(2, t = 0 .. modp(2-1, 3))); FB := sum(modp(5, product(2, t = 0 .. modp(q-1, 3))), q = 1 .. 2)

10

(1)

FC := modp(5, product(2, t = 0 .. modp(0, 3)))+modp(5, product(2, t = 0 .. modp(1, 3))); FD := sum(modp(5, product(2, t = 0 .. modp(q, 3))), q = 0 .. 1)

2

(2)

NULL

FA := modp(5, product(2, t = 0 .. modp(1 - 1, 3))) + modp(5, product(2, t = 0 .. modp(2 - 1, 3)));

2

(3)

 

FB := sum(modp(5, product(2, t = 0 .. modp(q - 1, 3))), q = 1 .. 2);

10

(4)

 

FC := modp(5, product(2, t = 0 .. modp(0, 3))) + modp(5, product(2, t = 0 .. modp(1, 3)));

2

(5)

NULL

FD := sum(modp(5, product(2, t = 0 .. modp(q, 3))), q = 0 .. 1);

2

(6)

NULL

Download BugTestSimple.mw

How do I find the solutions "links" with only answers in the range 0 to +1? The domain of vgl is 0 <=beta <= 1. If the system is inconsistent or insufficient to solve xi (for example, if xi does not appear in the equation) then give the text "no solution". If there is a solution then show it. Filter only real solutions. Please help me with better code:

restart;
assume(beta > 0, beta < 1):
interface(showassumed=0):

vgl[1] := -((beta*xi^2 + 2*xi^2 - beta)*(beta - 1)^2)/4 = 0:  # or some other equation (sometimes xi does not appear in the equation)

if has(lhs(vgl[1]), xi) or has(rhs(vgl[1]), xi) then
    links := solve([vgl[1], xi > 0, xi < beta], xi):
    # Filter only real solutions
    links_real := select(x -> type(x, equation) and is(Im(rhs(x)) = 0), [links]):
    if nops(links_real) > 0 then
        x1 := links_real;
        print("Real solution(s):", x1);
    else
        print("No real solution in range for xi.");
    end if;
else
    print("The equation does not contain xi — solving for xi is not possible.");
end if;

 

is it possible to ask Maple to verify ode solution obtained from book, which is given in parametric form to check if it is correct?

I know odetest supports both explicit and implicit solutions. But parametric solution is neither of these.

The solution in parametric form makes it look simple to look at and understand, but at same time, not practical in terms of obtaining an explicit solution to verify it and to use it.

The book "handbook of exact solution for ordinary differential equations" by Polyanin and Zaitsev have many such solutions.

Here is one such example of many

I can not just give odetest the y(x) solution above, because the right side depends on tau, which is parameter. If I try to solve for tau in terms of x from the first equation it will become so complicated and odetest hangs. So a whole new different approach is needed as brute force method is not practical in most cases.

restart;

ode:=y(x)*diff(y(x),x)-y(x)=A*x+B;
book_sol:=y(x)=_C1*t*exp( - Int( t/(t^2-t-A),t));
eq:=x=_C1*exp(  - Int( t/(t^2-t-A),t))-B/A;

y(x)*(diff(y(x), x))-y(x) = A*x+B

y(x) = _C1*t*exp(-(Int(t/(t^2-A-t), t)))

x = _C1*exp(-(Int(t/(t^2-A-t), t)))-B/A

value(eq):
solve(%,t):
simplify(eval(book_sol,t=%));

y(x) = _C1*exp(-RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z))+Intat(_a/(-_a^2+A+_a), _a = RootOf(-A*exp(2*RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))+_Z^2-exp(RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))*_Z+1)*exp(-RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))))*RootOf(-A*exp(2*RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))+_Z^2-exp(RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))*_Z+1)

odetest(%,ode); #hangs

Download how_to_verify_parametric_solution_to_ode.mw

Some more examples from the book where solutions are given only in parametrric form

update

inspired by solution below by @acer, I found if I just use Solve on the x equation, in order to find t as function of x, and use that in the y equation, it will automatically return solution using RootOf.

Hence no need to explicitly evaluate the integral or explicity set up the RootOf manually.

Now odetest work. 

restart;

ode:=y(x)*diff(y(x),x)-y(x)=A*x+B;
book_sol:=y(x)=_C1*t*exp( - Int( t/(t^2-t-A),t));
eq:=x=_C1*exp(  - Int( t/(t^2-t-A),t))-B/A;

y(x)*(diff(y(x), x))-y(x) = A*x+B

y(x) = _C1*t*exp(-(Int(t/(t^2-A-t), t)))

x = _C1*exp(-(Int(t/(t^2-A-t), t)))-B/A

PDEtools:-Solve(eq,t);

t = RootOf(c__1*exp(Intat(_a/(-_a^2+A+_a), _a = _Z))*A-A*x-B)

simplify(eval(book_sol,%));

y(x) = RootOf(c__1*exp(Intat(_a/(-_a^2+A+_a), _a = _Z))*A-A*x-B)*(A*x+B)/A

odetest(%,ode);

0

#compare to Maple's
simplify(dsolve(ode,useInt));

y(x) = -RootOf(-Intat(_a/(-_a^2+A-_a), _a = _Z)+Intat(1/_a, _a = A*x+B)+c__1)*(A*x+B)/A

odetest(%,ode);

0

 

 

Download how_to_verify_parametric_solution_to_ode_V2.mw

i seperate my equation of real part and imaginary part i want  after taking integrale from my real part we see the pattern betwen real and imaginary part  which they equal about variable beside coefficient , i want to determine and find parameter from real part of my equation then substitute in imaginary for solving but  the number of condition i don't know is how much and there is a little bit repeatation how i can determine the correct one and then substitute ?

restart

with(PDEtools)

undeclare(prime, quiet)

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet)

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

(1)

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

xi = -t*v+x

 

u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

(2)

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

(3)

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k*(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*k*w*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*w^2*exp(I*k*(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k*(t*w+x))+(2*I)*(D(U))(-t*v+x)*k*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-((D@@5)(U))(-t*v+x)*v*exp(I*k*(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*k^3*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*w*exp(I*k*(t*w+x))+6*((D@@3)(U))(-t*v+x)*v*k^2*exp(I*k*(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*k*exp(I*k*(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*k^3*w*exp(I*k*(t*w+x))-(D(U))(-t*v+x)*v*k^4*exp(I*k*(t*w+x))+I*((D@@4)(U))(-t*v+x)*k*w*exp(I*k*(t*w+x))-4*((D@@3)(U))(-t*v+x)*k^2*w*exp(I*k*(t*w+x))+4*(D(U))(-t*v+x)*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*(((D@@5)(U))(-t*v+x)*exp(I*k*(t*w+x))+(5*I)*((D@@4)(U))(-t*v+x)*k*exp(I*k*(t*w+x))-10*((D@@3)(U))(-t*v+x)*k^2*exp(I*k*(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*k^3*exp(I*k*(t*w+x))+5*(D(U))(-t*v+x)*k^4*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*w*exp(I*k*(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x)*v-beta*s*(c[2]*((D(U))(-t*v+x)*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*exp(I*k*(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x))

(4)

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi)))

(5)

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))) = 0

(6)

numer(lhs(pde1))*denom(rhs(pde1)) = numer(rhs(pde1))*denom(lhs(pde1))

-exp(I*k*(t*w+x))*((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2) = 0

(7)

%/(-exp(I*k*(t*w+x)))

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2 = 0

(8)

Re(%)

Re((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1])-Im(-24*U(xi)*k^2*s^2+24*U(xi)*k^2*w^2+24*U(xi)*alpha*k^5*s*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+24*U(xi)^3*beta*k*s*c[2]+120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]-U(xi)*k^5*w*c[1]-4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-24*U(xi)^3*k*w*c[2]+4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]+24*(diff(diff(U(xi), xi), xi))*s^2-24*(diff(diff(U(xi), xi), xi))*v^2) = 0

(9)

R := (diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

(10)

collect(R, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0

(11)

map(int, (72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0, xi)

(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0

(12)

numer(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0)) = numer(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))

120*U(xi)*alpha*k^4*s*c[1]+U(xi)*k^4*v*c[1]-4*U(xi)*k^4*w*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^2*s*c[1]+24*U(xi)^3*beta*s*c[2]-6*(diff(diff(U(xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(U(xi), xi), xi))*k^2*w*c[1]+24*U(xi)^3*v*c[2]+24*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*s*c[1]-48*U(xi)*k*s^2-48*U(xi)*k*v*w+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*c[1] = 0

(13)

RR := collect(%, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(24*beta*s*c[2]+24*v*c[2])*U(xi)^3+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

(14)

IM := 24*U(xi)*k^2*s^2-24*U(xi)*k^2*w^2-24*U(xi)*alpha*k^5*s*c[1]+240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]-24*U(xi)^3*beta*k*s*c[2]-120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+U(xi)*k^5*w*c[1]+4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]-6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]+24*U(xi)^3*k*w*c[2]-4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-24*(diff(diff(U(xi), xi), xi))*s^2+24*(diff(diff(U(xi), xi), xi))*v^2 = 0

collect(IM, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

P := %

(-24*beta*k*s*c[2]+24*k*w*c[2])*U(xi)^3+(-24*alpha*k^5*s*c[1]+k^5*w*c[1]+24*k^2*s^2-24*k^2*w^2)*U(xi)+(240*alpha*k^3*s*c[1]+4*k^3*v*c[1]-6*k^3*w*c[1]-24*s^2+24*v^2)*(diff(diff(U(xi), xi), xi))+(-120*alpha*k*s*c[1]-4*k*v*c[1]+k*w*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

(15)

NULL

NULL

C1 := v = solve(24*beta*s*c[2]+24*v*c[2] = 0, v)

v = -beta*s

(16)

C2 := w = solve(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w = 0, w)

w = (1/4)*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)/(k^3*c[1]+12*v)

(17)

C3 := alpha = solve(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1] = 0, alpha)

alpha = -(1/120)*(3*v-2*w)/s

(18)

ode1 := subs({C1, C2, C3}, P)

(-24*beta*k*s*c[2]+6*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[2]/(k^3*c[1]+12*v))*U(xi)^3+((1/5)*(3*v-2*w)*k^5*c[1]+(1/4)*k^5*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)+24*k^2*s^2-(3/2)*k^2*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)^2/(k^3*c[1]+12*v)^2)*U(xi)+(-2*(3*v-2*w)*k^3*c[1]-4*k^3*beta*s*c[1]-(3/2)*k^3*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)-24*s^2+24*beta^2*s^2)*(diff(diff(U(xi), xi), xi))+((3*v-2*w)*k*c[1]+4*k*beta*s*c[1]+(1/4)*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

(19)

Download F-condition_and_replacing.mw

I am not sure how to use dsolve for my problem.
CQ_v1.mw

Is there a trick to make Maple simplify 

to

I can't use the exp() trick given in earlier questions, since there is no exp here. Below are my attempts. Can someone find another smart trick to do this simplification? Should simplify() have simplified it as is with no assumptions or using tricks? This is all done in code, so solutions can not depend on "looking on screen" and deciding what to do for each step.

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

restart;

interface(rtablesize=30);

[10, 10]

A:=-(sqrt(3)*sqrt(-2*C1 - 2*x) - 3)/(3*sqrt(-2*C1 - 2*x)*x);

-(1/3)*(3^(1/2)*(-2*C1-2*x)^(1/2)-3)/((-2*C1-2*x)^(1/2)*x)

B:=-(1/(sqrt(3)*x)) + 1/(sqrt(2)*x*sqrt(-x - C1));

-(1/3)*3^(1/2)/x+(1/2)*2^(1/2)/(x*(-x-C1)^(1/2))

simplify(A-B);

0

MmaTranslator:-Mma:-LeafCount(A);
MmaTranslator:-Mma:-LeafCount(B);

29

26

full_simplify:=proc(e::anything,assum::anything)
   local result::list;

   #add more methods as needed

   result:=[(simplify(e) assuming assum),
            (simplify(e,size=false) assuming assum),
            (simplify(e,size) assuming assum),
            (simplify(e,sqrt) assuming assum),
            (simplify(combine(e)) assuming assum),
            (simplify(combine(e),size) assuming assum),
            (radnormal(evala( combine(e) )) assuming assum),
            (simplify(evala( combine(e) )) assuming assum),
            (evala(radnormal( combine(e) )) assuming assum),
            (simplify(radnormal( combine(e) )) assuming assum),
            (evala(factor(e)) assuming assum),
            (simplify(e,ln) assuming assum),
            (simplify(e,power) assuming assum),
            (simplify(e,RootOf) assuming assum),
            (simplify(e,sqrt) assuming assum),
            (simplify(e,trig) assuming assum),
            (simplify(convert(e,trig)) assuming assum),
            (simplify(convert(e,exp)) assuming assum),
            (combine(e) assuming assum)
   ];   
   RETURN( result )

end proc:

Vector(full_simplify(A,real))

Vector(19, {(1) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (2) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (3) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (4) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (5) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (6) = -(1/3)*(sqrt(-6*C1-6*x)-3)/(sqrt(-2*C1-2*x)*x), (7) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(-6*C1-6*x)-3)/((C1+x)*x), (8) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/((C1+x)*x), (9) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(-6*C1-6*x)-3)/((C1+x)*x), (10) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (11) = -(1/6)*(2*sqrt(3)*C1+2*sqrt(3)*x+3*sqrt(-2*C1-2*x))/((C1+x)*x), (12) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (13) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (14) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (15) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (16) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (17) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (18) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (19) = -(1/3)*(sqrt(-6*C1-6*x)-3)/(sqrt(-2*C1-2*x)*x)})

Vector(full_simplify(A,positive))

Vector(19, {(1) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (2) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (3) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (4) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (5) = (1/3)*(-sqrt(3)*sqrt(2*C1+2*x)-3*I)/(sqrt(2*C1+2*x)*x), (6) = -(1/3)*(I*sqrt(6*C1+6*x)-3)/(sqrt(-2*C1-2*x)*x), (7) = (1/6)*sqrt(-2*C1-2*x)*(I*sqrt(6*C1+6*x)-3)/((C1+x)*x), (8) = -(1/6)*sqrt(2*C1+2*x)*(sqrt(3)*sqrt(2*C1+2*x)+3*I)/((C1+x)*x), (9) = (1/6)*sqrt(-2*C1-2*x)*(I*sqrt(6*C1+6*x)-3)/((C1+x)*x), (10) = (1/3)*(-sqrt(3)*sqrt(2*C1+2*x)-3*I)/(sqrt(2*C1+2*x)*x), (11) = -(1/6)*(2*sqrt(3)*C1+2*sqrt(3)*x+3*sqrt(-2*C1-2*x))/((C1+x)*x), (12) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (13) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (14) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (15) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (16) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (17) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (18) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (19) = -(1/3)*(I*sqrt(6*C1+6*x)-3)/(sqrt(-2*C1-2*x)*x)})

 

 

Download simplification_may_8_2025.mw

For reference, using another software

I'm trying to extract the real and imaginary parts of a given PDE. However, during the substitution step, something unexpected occurs. Specifically, my replacement does not yield the expected result, and an extra term appears: D(k)(t*w + x) in the expression P11. I'm unsure why this term arises and would appreciate any insight into what might be going wrong during the substitution process.

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

(1)

declare(u(x, t)); declare(U(xi)); declare(V(xi))

u(x, t)*`will now be displayed as`*u

 

U(xi)*`will now be displayed as`*U

 

V(xi)*`will now be displayed as`*V

(2)

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), t)-beta*s*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), x)

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v+c[3]*(diff(u(x, t), t))*U(-t*v+x)^4-4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)*v+c[4]*(diff(u(x, t), t))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)+c[3]*(diff(u(x, t), x))*U(-t*v+x)^4+4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)+c[4]*(diff(u(x, t), x))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

(3)

``

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))

U(-t*v+x) = U(xi)

 

(D(U))(-t*v+x) = diff(U(xi), xi)

 

((D@@2)(U))(-t*v+x) = diff(diff(U(xi), xi), xi)

 

((D@@3)(U))(-t*v+x) = diff(diff(diff(U(xi), xi), xi), xi)

 

((D@@4)(U))(-t*v+x) = diff(diff(diff(diff(U(xi), xi), xi), xi), xi)

 

((D@@5)(U))(-t*v+x) = diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)

(4)

NULL

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k(t*w+x))

xi = -t*v+x

 

u(x, t) = U(-t*v+x)*exp(I*k(t*w+x))

(5)

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), t)-beta*s*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2+c[3]*u(x, t)*U(-t*v+x)^4+c[4]*u(x, t)*(diff(U(-t*v+x)^2, `$`(x, 2))), x)

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v+c[3]*(diff(u(x, t), t))*U(-t*v+x)^4-4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)*v+c[4]*(diff(u(x, t), t))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)+c[3]*(diff(u(x, t), x))*U(-t*v+x)^4+4*c[3]*u(x, t)*U(-t*v+x)^3*(D(U))(-t*v+x)+c[4]*(diff(u(x, t), x))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*u(x, t)*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

(6)

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(-t*v+x)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k(t*w+x))+(2*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*((D@@3)(U))(-t*v+x)*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(D(U))(-t*v+x)*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))-(24*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(D(U))(-t*v+x)*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+12*((D@@2)(U))(-t*v+x)*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(-t*v+x)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-12*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(D(U))(-t*v+x)*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+3*(D(U))(-t*v+x)*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+(4*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*((D@@3)(U))(-t*v+x)*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*((D@@2)(U))(-t*v+x)*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(D(U))(-t*v+x)*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-((D@@5)(U))(-t*v+x)*v*exp(I*k(t*w+x)))-alpha*s*c[1]*(I*U(-t*v+x)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(30*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+((D@@5)(U))(-t*v+x)*exp(I*k(t*w+x))+5*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k(t*w+x))*(D(U))(-t*v+x)*v+c[3]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(-t*v+x)^4-4*c[3]*U(-t*v+x)^4*exp(I*k(t*w+x))*(D(U))(-t*v+x)*v+c[4]*(-(D(U))(-t*v+x)*v*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*U(-t*v+x)*exp(I*k(t*w+x))*(-6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)*v-2*U(-t*v+x)*((D@@3)(U))(-t*v+x)*v)-beta*s*(I*U(-t*v+x)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*((D@@2)(U))(-t*v+x)*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(30*I)*(D(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*((D@@4)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(-t*v+x)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(D(U))(-t*v+x)*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(-t*v+x)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(D(U))(-t*v+x)*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(-t*v+x)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(D(U))(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*((D@@2)(U))(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(-t*v+x)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(-t*v+x)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*((D@@3)(U))(-t*v+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+((D@@5)(U))(-t*v+x)*exp(I*k(t*w+x))+5*(D(U))(-t*v+x)*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*((D@@3)(U))(-t*v+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k(t*w+x))*(D(U))(-t*v+x)+c[3]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(-t*v+x)^4+4*c[3]*U(-t*v+x)^4*exp(I*k(t*w+x))*(D(U))(-t*v+x)+c[4]*((D(U))(-t*v+x)*exp(I*k(t*w+x))+I*U(-t*v+x)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(D(U))(-t*v+x)^2+2*U(-t*v+x)*((D@@2)(U))(-t*v+x))+c[4]*U(-t*v+x)*exp(I*k(t*w+x))*(6*(D(U))(-t*v+x)*((D@@2)(U))(-t*v+x)+2*U(-t*v+x)*((D@@3)(U))(-t*v+x))

(7)

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)NULL

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi)))

(8)

``

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0

(9)

numer(lhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))*denom(rhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0)) = numer(rhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))*denom(lhs(I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k(t*w+x))-(2*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*w^2*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*w^2*exp(I*k(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k(t*w+x))+(2*I)*(diff(U(xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-U(xi)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*(D(k))(t*w+x)^4*w*exp(I*k(t*w+x))-12*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*w*exp(I*k(t*w+x))+3*(diff(U(xi), xi))*v*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))-(diff(U(xi), xi))*v*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*w*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))+4*(diff(U(xi), xi))*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-I*(diff(U(xi), xi))*v*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))-(6*I)*(diff(diff(diff(U(xi), xi), xi), xi))*v*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(U(xi), xi), xi))*v*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*w*exp(I*k(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*w*exp(I*k(t*w+x))+(6*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*w*exp(I*k(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+12*(diff(diff(U(xi), xi), xi))*v*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-18*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+10*U(xi)*(D(k))(t*w+x)^3*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-16*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*w*(D(k))(t*w+x)*exp(I*k(t*w+x))+(6*I)*(diff(U(xi), xi))*v*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*w*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*w*(D(k))(t*w+x)*exp(I*k(t*w+x))-(24*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*w*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x))-alpha*s*c[1]*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^2-2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*v*c[2]+c[3]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*U(xi)^4-4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*v*c[3]+c[4]*(-(diff(U(xi), xi))*v*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*w*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(-6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))*v-2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))*v)-beta*s*(-(10*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*exp(I*k(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))+(10*I)*(diff(diff(U(xi), xi), xi))*((D@@3)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*((D@@5)(k))(t*w+x)*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)^5*exp(I*k(t*w+x))-10*U(xi)*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-15*(diff(U(xi), xi))*((D@@2)(k))(t*w+x)^2*exp(I*k(t*w+x))+10*U(xi)*(D(k))(t*w+x)^3*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(10*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*exp(I*k(t*w+x))-5*U(xi)*((D@@4)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-20*(diff(U(xi), xi))*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*exp(I*k(t*w+x))-30*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(5*I)*(diff(U(xi), xi))*((D@@4)(k))(t*w+x)*exp(I*k(t*w+x))-(15*I)*U(xi)*((D@@2)(k))(t*w+x)^2*(D(k))(t*w+x)*exp(I*k(t*w+x))-(10*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*exp(I*k(t*w+x))-(30*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x))*((D@@2)(k))(t*w+x)+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k(t*w+x))+5*(diff(U(xi), xi))*(D(k))(t*w+x)^4*exp(I*k(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2*exp(I*k(t*w+x)))+c[2]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^2+2*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^2*c[2]+c[3]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*U(xi)^4+4*exp(I*k(t*w+x))*(diff(U(xi), xi))*U(xi)^4*c[3]+c[4]*((diff(U(xi), xi))*exp(I*k(t*w+x))+I*U(xi)*(D(k))(t*w+x)*exp(I*k(t*w+x)))*(2*(diff(U(xi), xi))^2+2*U(xi)*(diff(diff(U(xi), xi), xi)))+c[4]*U(xi)*exp(I*k(t*w+x))*(6*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+2*U(xi)*(diff(diff(diff(U(xi), xi), xi), xi))) = 0))

-exp(I*k(t*w+x))*(-I*U(xi)*(D(k))(t*w+x)^5*c[1]*w-(4*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*c[1]*v+(6*I)*c[1]*w*(D(k))(t*w+x)^3*(diff(diff(U(xi), xi), xi))+(4*I)*c[1]*v*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-(6*I)*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))*c[1]*w-(4*I)*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))*c[1]*w+(4*I)*c[1]*v*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)*c[1]*w-I*U(xi)*((D@@5)(k))(t*w+x)*c[1]*w+(6*I)*c[1]*v*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(4*I)*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)*c[1]*w+(24*I)*s*beta*U(xi)*(D(k))(t*w+x)^5-(240*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*beta*s+(240*I)*s*beta*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+(120*I)*s*beta*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))+(120*I)*s*beta*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)+(24*I)*s*beta*((D@@5)(k))(t*w+x)*U(xi)+(240*I)*s*beta*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(48*I)*U(xi)^2*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*c[4]-(48*I)*U(xi)*(diff(U(xi), xi))^2*(D(k))(t*w+x)*c[4]-(24*I)*c[2]*w*U(xi)^3*(D(k))(t*w+x)-(24*I)*c[3]*w*U(xi)^5*(D(k))(t*w+x)+24*c[1]*s*alpha*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))+48*c[4]*v*(diff(diff(diff(U(xi), xi), xi), xi))*U(xi)^2+c[1]*v*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))+24*s*beta*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))-48*c[4]*(diff(diff(diff(U(xi), xi), xi), xi))*U(xi)^2+I*c[1]*v*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))-10*c[1]*w*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-12*c[1]*v*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+18*c[1]*w*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-4*c[1]*v*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))+16*c[1]*w*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))+5*c[1]*w*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)+10*c[1]*w*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)+120*c[1]*s*alpha*(D(k))(t*w+x)^4*(diff(U(xi), xi))-360*c[1]*s*alpha*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-240*c[1]*s*alpha*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+192*c[4]*v*U(xi)*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))+240*s*beta*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-720*s*beta*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-480*s*beta*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))-120*s*beta*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)-240*s*beta*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)-(240*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*c[1]*alpha*s-(360*I)*U(xi)*(D(k))(t*w+x)*((D@@2)(k))(t*w+x)^2*c[1]*alpha*s-(720*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*c[1]*alpha*s+240*c[1]*s*alpha*((D@@2)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^3-720*c[1]*s*alpha*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)*(diff(diff(U(xi), xi), xi))-480*c[1]*s*alpha*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)*(diff(U(xi), xi))-120*c[1]*s*alpha*((D@@4)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)-240*c[1]*s*alpha*((D@@3)(k))(t*w+x)*((D@@2)(k))(t*w+x)*U(xi)+(15*I)*c[1]*w*((D@@2)(k))(t*w+x)^2*U(xi)*(D(k))(t*w+x)+(24*I)*c[1]*s*alpha*U(xi)*(D(k))(t*w+x)^5-(240*I)*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)^3*c[1]*alpha*s+(240*I)*c[1]*s*alpha*((D@@3)(k))(t*w+x)*(diff(diff(U(xi), xi), xi))+(120*I)*c[1]*s*alpha*((D@@4)(k))(t*w+x)*(diff(U(xi), xi))+(120*I)*c[1]*s*alpha*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*(D(k))(t*w+x)+(24*I)*c[1]*s*alpha*((D@@5)(k))(t*w+x)*U(xi)+(240*I)*c[1]*s*alpha*(diff(diff(diff(U(xi), xi), xi), xi))*((D@@2)(k))(t*w+x)-(48*I)*U(xi)^2*(diff(diff(U(xi), xi), xi))*(D(k))(t*w+x)*c[4]*w-48*c[4]*(diff(U(xi), xi))^3-(48*I)*U(xi)*(diff(U(xi), xi))^2*(D(k))(t*w+x)*c[4]*w-(720*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*beta*s-(240*I)*U(xi)*((D@@3)(k))(t*w+x)*(D(k))(t*w+x)^2*beta*s-(360*I)*U(xi)*(D(k))(t*w+x)*((D@@2)(k))(t*w+x)^2*beta*s-(6*I)*(diff(U(xi), xi))*(D(k))(t*w+x)^2*((D@@2)(k))(t*w+x)*c[1]*v+(24*I)*c[1]*w*((D@@2)(k))(t*w+x)*(D(k))(t*w+x)^2*(diff(U(xi), xi))+(10*I)*c[1]*w*((D@@3)(k))(t*w+x)*U(xi)*(D(k))(t*w+x)^2-(24*I)*s^2*U(xi)*(D(k))(t*w+x)^2-(24*I)*c[2]*U(xi)^3*(D(k))(t*w+x)-(24*I)*c[3]*U(xi)^5*(D(k))(t*w+x)+(24*I)*w^2*U(xi)*(D(k))(t*w+x)^2+24*w^2*((D@@2)(k))(t*w+x)*U(xi)+c[1]*v*(D(k))(t*w+x)^4*(diff(U(xi), xi))-4*c[1]*w*(D(k))(t*w+x)^4*(diff(U(xi), xi))-3*c[1]*v*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))+12*c[1]*w*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-6*c[1]*v*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+4*c[1]*w*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2+72*c[2]*v*U(xi)^2*(diff(U(xi), xi))+120*c[3]*v*U(xi)^4*(diff(U(xi), xi))+120*s*beta*(D(k))(t*w+x)^4*(diff(U(xi), xi))-360*s*beta*((D@@2)(k))(t*w+x)^2*(diff(U(xi), xi))-240*s*beta*(diff(diff(diff(U(xi), xi), xi), xi))*(D(k))(t*w+x)^2-192*c[4]*U(xi)*(diff(U(xi), xi))*(diff(diff(U(xi), xi), xi))-48*w*(D(k))(t*w+x)*v*(diff(U(xi), xi))-(24*I)*v^2*(diff(diff(U(xi), xi), xi))+(24*I)*s^2*(diff(diff(U(xi), xi), xi))-48*s^2*(D(k))(t*w+x)*(diff(U(xi), xi))-24*s^2*((D@@2)(k))(t*w+x)*U(xi)+48*c[4]*v*(diff(U(xi), xi))^3-72*c[2]*U(xi)^2*(diff(U(xi), xi))-120*c[3]*U(xi)^4*(diff(U(xi), xi))) = 0

(10)

%/(-exp(I*k(t*w+x)))

-()/exp(k(t*w+x)*I)

(11)
 

``

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