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why i can't remove the the denominatore ...

Math-dashti 135 Maple 2024
denominator duplicate-account
November 14 2025
1 11

is work for some equation but sometime is make problem and again make it problem for me where is problem why the denominator of second equation still remain while i want to remove it i times by denominator but still not worked

in my orginal ode i did change the place diff(V(xi),xi)=Omega(xi) maybe make problem ...or not

like this equation but the equation is different

> 

restart
> 

with(PDEtools)
> 

with(plots)
> 

with(plots):
> 

with(DEtools):
> 

undeclare(prime, quiet)
> 

with(LinearAlgebra)
> 

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

ode := -(8*(1/4+k^2*alpha[1]^2+((1/2)*w^2*alpha[2]-k)*alpha[1]))*V(xi)*(diff(Omega(xi), xi))+(4*k^2*alpha[1]^2+1+(2*w^2*alpha[2]-4*k)*alpha[1])*Omega(xi)^2+8*w^2*(-alpha[4]*V(xi)^2+k^2*alpha[1]+(1/2)*w^2*alpha[2]-alpha[3]*V(xi)-k)*alpha[2]*V(xi)^2 = 0

-8*(1/4+k^2*alpha[1]^2+((1/2)*w^2*alpha[2]-k)*alpha[1])*V(xi)*(diff(Omega(xi), xi))+(4*k^2*alpha[1]^2+1+(2*w^2*alpha[2]-4*k)*alpha[1])*Omega(xi)^2+8*w^2*(-alpha[4]*V(xi)^2+k^2*alpha[1]+(1/2)*w^2*alpha[2]-alpha[3]*V(xi)-k)*alpha[2]*V(xi)^2 = 0

 (1)
> 

NULL
> 

raw := DEtools[convertsys]({ode}, {}, Omega(xi), xi, s, QP, QP)[1..2];

[[QP[1] = -(1/8)*(-(4*k^2*alpha[1]^2+1+(2*w^2*alpha[2]-4*k)*alpha[1])*s[1]^2-8*w^2*(-alpha[4]*V(xi)^2+k^2*alpha[1]+(1/2)*w^2*alpha[2]-alpha[3]*V(xi)-k)*alpha[2]*V(xi)^2)/((1/4+k^2*alpha[1]^2+((1/2)*w^2*alpha[2]-k)*alpha[1])*V(xi))], [s[1] = Omega(xi)]]

 (2)

Extract the denominator and scale the right hand sides by it

> 

den:=denom(eval(QP[2],raw[1]));
raw_eta:=map(q->rhs(q)*den,raw[1]);

1

  

[-(1/8)*(-(4*k^2*alpha[1]^2+1+(2*w^2*alpha[2]-4*k)*alpha[1])*s[1]^2-8*w^2*(-alpha[4]*V(xi)^2+k^2*alpha[1]+(1/2)*w^2*alpha[2]-alpha[3]*V(xi)-k)*alpha[2]*V(xi)^2)/((1/4+k^2*alpha[1]^2+((1/2)*w^2*alpha[2]-k)*alpha[1])*V(xi))]

 (3)

Back to the real transformed variables, which are now in terms of eta.

> 

rhs_eta := eval(raw_eta, {s[1] = phi(eta), s[2] = y(eta)})

[2*y(eta)*(4*k^2*alpha[1]^2+2*w^2*alpha[1]*alpha[2]-4*k*alpha[1]+1)*phi(eta), -(1/4)*(-(4*k^2*alpha[1]^2+1+(2*w^2*alpha[2]-4*k)*alpha[1])*y(eta)^2-8*w^2*(-alpha[4]*phi(eta)^2+k^2*alpha[1]+(1/2)*w^2*alpha[2]-alpha[3]*phi(eta)-k)*alpha[2]*phi(eta)^2)*(4*k^2*alpha[1]^2+2*w^2*alpha[1]*alpha[2]-4*k*alpha[1]+1)/(1/4+k^2*alpha[1]^2+((1/2)*w^2*alpha[2]-k)*alpha[1])]

 (4)

Find equilibrium points - one is at the origin; the others are a complicated mess.

> 

equilibria := [solve(rhs_eta, {phi(eta), y(eta)}, explicit)]; nops(%)

3

 (5)

Eq 9.

> 

de1 := diff(phi(eta), eta) = rhs_eta[1]; de2 := diff(y(eta), eta) = rhs_eta[2]

diff(phi(eta), eta) = 2*y(eta)*(4*k^2*alpha[1]^2+2*w^2*alpha[1]*alpha[2]-4*k*alpha[1]+1)*phi(eta)

  

diff(y(eta), eta) = -(1/4)*(-(4*k^2*alpha[1]^2+1+(2*w^2*alpha[2]-4*k)*alpha[1])*y(eta)^2-8*w^2*(-alpha[4]*phi(eta)^2+k^2*alpha[1]+(1/2)*w^2*alpha[2]-alpha[3]*phi(eta)-k)*alpha[2]*phi(eta)^2)*(4*k^2*alpha[1]^2+2*w^2*alpha[1]*alpha[2]-4*k*alpha[1]+1)/(1/4+k^2*alpha[1]^2+((1/2)*w^2*alpha[2]-k)*alpha[1])

 (6)
> 

PDEtools:-ConservedCurrents({de1, de2}, [phi(eta), y(eta)]); P1 := -(1/2)*op(1, rhs(op(%)))

[_J[eta](eta, phi(eta), y(eta)) = f__1((1/3)*(2*w^2*alpha[2]*phi(eta)^4*alpha[4]+3*w^2*alpha[2]*phi(eta)^3*alpha[3]-6*(k^2*alpha[1]+(1/2)*w^2*alpha[2]-k)*alpha[2]*w^2*phi(eta)^2+3*((1/2)*w^2*alpha[1]*alpha[2]+(k*alpha[1]-1/2)^2)*y(eta)^2)/(((1/2)*w^2*alpha[1]*alpha[2]+(k*alpha[1]-1/2)^2)*phi(eta)), (1/2)*3^(1/2)*Intat(1/((-96*(-(1/3)*w^2*alpha[2]*phi(eta)^4*alpha[4]-(1/2)*w^2*alpha[2]*phi(eta)^3*alpha[3]+(k^2*alpha[1]+(1/2)*w^2*alpha[2]-k)*alpha[2]*w^2*phi(eta)^2-_a*(k^2*alpha[1]+(1/2)*w^2*alpha[2]-(1/3)*_a^2*alpha[4]-(1/2)*_a*alpha[3]-k)*w^2*alpha[2]*phi(eta)-(1/2)*((1/2)*w^2*alpha[1]*alpha[2]+(k*alpha[1]-1/2)^2)*y(eta)^2)*_a*((1/2)*w^2*alpha[1]*alpha[2]+(k*alpha[1]-1/2)^2)/phi(eta))^(1/2)*_a), _a = phi(eta))+eta)]

  

-(1/6)*(2*w^2*alpha[2]*phi(eta)^4*alpha[4]+3*w^2*alpha[2]*phi(eta)^3*alpha[3]-6*(k^2*alpha[1]+(1/2)*w^2*alpha[2]-k)*alpha[2]*w^2*phi(eta)^2+3*((1/2)*w^2*alpha[1]*alpha[2]+(k*alpha[1]-1/2)^2)*y(eta)^2)/(((1/2)*w^2*alpha[1]*alpha[2]+(k*alpha[1]-1/2)^2)*phi(eta))

 (7)

NULL

Download make_system.mw

why can't i solve for my parameters?...

Math-dashti 135 Maple 2024
solve duplicate-question duplicate-account
November 13 2025
1 5

in here i have 4 equations and i want to find 4 parameter can anyone say where is problem?

> 

NULL
> 

restart
> 

eq1 := S__1 = sqrt((-beta[1]+sqrt(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2))/beta[2]); eq2 := S__2 = (1/2)*sqrt(-(2*(beta[1]+sqrt(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)))/beta[2]); eq3 := S__3 = sqrt(2)*sqrt(chi*(4*chi^2*k^2*p+4*chi^2*w+2*chi*p*beta[1]-p^2*beta[2]))/(4*chi^2); eq4 := T__1 = sqrt(-2*chi*p)/(2*chi); eqs := {eq1, eq2, eq3, eq4}

S__1 = ((-beta[1]+(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2))/beta[2])^(1/2)

  

S__2 = (1/2)*(-2*(beta[1]+(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2))/beta[2])^(1/2)

  

S__3 = (1/4)*2^(1/2)*(chi*(4*chi^2*k^2*p+4*chi^2*w+2*chi*p*beta[1]-p^2*beta[2]))^(1/2)/chi^2

  

T__1 = (1/2)*(-2*chi*p)^(1/2)/chi

  

{S__1 = ((-beta[1]+(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2))/beta[2])^(1/2), S__2 = (1/2)*(-2*(beta[1]+(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2))/beta[2])^(1/2), S__3 = (1/4)*2^(1/2)*(chi*(4*chi^2*k^2*p+4*chi^2*w+2*chi*p*beta[1]-p^2*beta[2]))^(1/2)/chi^2, T__1 = (1/2)*(-2*chi*p)^(1/2)/chi}

 (1)
> 

indets(eqs)

{S__1, S__2, S__3, T__1, chi, k, p, w, beta[1], beta[2], (chi*(4*chi^2*k^2*p+4*chi^2*w+2*chi*p*beta[1]-p^2*beta[2]))^(1/2), ((-beta[1]+(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2))/beta[2])^(1/2), (-2*chi*p)^(1/2), (-2*(beta[1]+(4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2))/beta[2])^(1/2), (4*k^2*p*beta[2]+4*w*beta[2]+beta[1]^2)^(1/2)}

 (2)

We have 4 eqns, so choose 2  variables to solve for

> 

eval(eqs, {S__1 = 1, S__2 = 1, S__3 = 1, T__1 = 1, k = 1, p = 1}); sol := solve(%, {chi, w, beta[1], beta[2]})

{1 = ((-beta[1]+(4*w*beta[2]+beta[1]^2+4*beta[2])^(1/2))/beta[2])^(1/2), 1 = (1/2)*(-2*(beta[1]+(4*w*beta[2]+beta[1]^2+4*beta[2])^(1/2))/beta[2])^(1/2), 1 = (1/2)*(-2*chi)^(1/2)/chi, 1 = (1/4)*2^(1/2)*(chi*(4*chi^2*w+4*chi^2+2*chi*beta[1]-beta[2]))^(1/2)/chi^2}

  

(3)
NULL

Download find-parameter.mw

How can I produce phase-portrait and jac...

Math-dashti 135 Maple 2024
parameter differential-equations phaseportrait
November 12 2025
1 5

in this equation i can't do phase portrait and visualization and invistagation of thus point are really not easy which i do a lot substitution for do more simplify but still not work, i want to do phase portrait for thus point but the parameter are too much and each time i have to determine my point which behavior have for each point i have to know the jacobian of them and each time i have to change the parameter to be biger or smaller than zero so i have to replace thus point to be something very easy like A or B  but i don't know how to do that i need an expert to help me , i did my best in file but i can't finished

f2.mw

System of ODEs, conserved quantity, alon...

Math-dashti 135 Maple 2024
ode differential-equations jacobian
September 27 2025
1 3

in here i want the system which when i found the system it contain a singularity but by some changing of system we can remove it, i know how he did that but i can't do it by coding, also after removing which i did by hand , there is another problem which equalibruiom points is to long how i can make it be shorter becuase contain two function i don't know how do that can i change the coiefecient of any function by another letter? also for phase portrait i need `conserved quantity` which last code is not work for finding this kind of system ? and how decide about jacobian if the `conserved quantity` is know by that after determine the points it will be clear on plots, i write the code untill finding the `conserved quantity` becuase code not run i didn't find jacobian and phase portrait but i will put the code of jacobian and phase portrait too! 

bi-1.mw

How fix the issue of this plotting?...

Math-dashti 135 Maple 2024
explore dsolve numeric
September 08 2025
0 6

i don't  know  why my graph make a problem and what is issue i did plot  but this time make issue for me which i don't know where is problem there is anyone which can help and even modified the plot?

explore-chaotic.mw

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