matmxhu

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8 years, 162 days

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These are replies submitted by matmxhu

@dharr thanks,yes,i know the exact answer, but how to  avoid the problem caused by interval if  no warning message was given.

@vv thanks a lot

@Preben Alsholm thanks a lot

@ThU for indexed subscripts,i can use indets(poly,'specindex(anything,a)') to acquire a[b], and use "select(has, poly,a[b])" to reach the results,but now,i meet  literal subscripts rather than indexed subscripts,how do i?

@EugeneKalentev 

 

 

thanks a lot ,i find you wrote p[2] rather than p2.

NULL

NULL

``

with(PDEtools):

PDE := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2]);

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

(1)

pdsolve(PDE)

`Warning:  Incomplete separation.`

 

______________________________________________________

 

` `

 

PDESolStruc(f(x[1], x[2], p[1], p[2]) = _F4(p[2])+_F5(x[1], x[2], p[1]), [{-2*(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[1]+(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[2]+k*_c[4]*x[1]*m-2*k*_c[4]*x[2]*m+(diff(_F5(x[1], x[2], p[1]), x[1]))*p[1]+(diff(_F5(x[1], x[2], p[1]), x[2]))*p__2 = 0, diff(_F4(p[2]), p[2]) = _c[4]}])

(2)

NULL

PDE1 := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p[2]/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p[2]/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

(3)

pdsolve(PDE1)

PDE2 := (diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2]);

(diff(f(x[1], x[2], p[1], p[2]), x[1]))*p[1]/m-(diff(f(x[1], x[2], p[1], p[2]), p[1]))*(2*k*x[1]-k*x[2])+(diff(f(x[1], x[2], p[1], p[2]), x[2]))*p__2/m-(diff(f(x[1], x[2], p[1], p[2]), p[2]))*(-k*x[1]+2*k*x[2])

(4)

pdsolve(PDE2)

`Warning:  Incomplete separation.`

 

______________________________________________________

 

` `

 

PDESolStruc(f(x[1], x[2], p[1], p[2]) = _F4(p[2])+_F5(x[1], x[2], p[1]), [{-2*(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[1]+(diff(_F5(x[1], x[2], p[1]), p[1]))*k*m*x[2]+k*_c[4]*x[1]*m-2*k*_c[4]*x[2]*m+(diff(_F5(x[1], x[2], p[1]), x[1]))*p[1]+(diff(_F5(x[1], x[2], p[1]), x[2]))*p__2 = 0, diff(_F4(p[2]), p[2]) = _c[4]}])

(5)

``

``

From PDE2,we can see p2 different from p[2],i guess the result should be symmetry rather than Eq.(5)

``

``

``

``

``


Download 7.mw

@Markiyan Hirnyk 

hi,please see my attachment,i slove the equations using DirectSearch v.2,for some parameters ,it can work well,but when i choose some ones,it has been running so a great deal of time(one day and one night) that i'm not even sure solves exists.but once in a while,solves can be found,why? thanks  a lot.

``

restart; with(DirectSearch); Digits := 20

20

(1)

f := omega__a*alpha^2+omega__b*beta^2+Omega__a*eta^2+Omega__b*chi^2-2*kappa*alpha*beta-(1/2)*Omega__a-(1/2)*Omega__b-4*lambda__b*sqrt(-chi^2+1)*chi*beta-4*lambda__a*sqrt(-eta^2+1)*eta*alpha:

eq := sort([seq(diff(f, i), `in`(i, [alpha, beta, eta, chi]))], length)

[2*omega__a*alpha-2*kappa*beta-4*lambda__a*(-eta^2+1)^(1/2)*eta, 2*omega__b*beta-2*kappa*alpha-4*lambda__b*(-chi^2+1)^(1/2)*chi, 2*Omega__b*chi+4*lambda__b*chi^2*beta/(-chi^2+1)^(1/2)-4*lambda__b*(-chi^2+1)^(1/2)*beta, 2*Omega__a*eta+4*lambda__a*eta^2*alpha/(-eta^2+1)^(1/2)-4*lambda__a*(-eta^2+1)^(1/2)*alpha]

(2)

``

omega__a := 1;

1

 

1

 

1

 

1

 

.3

(3)

X := [seq((i-1)*0.3e-1, i = 1 .. 21)]

Y := [seq((i-1)*0.3e-1, i = 1 .. 21)]

X := [.27]:

.27

 

.57

(4)

sols1 := SolveEquations(map(proc (t) options operator, arrow; convert(t, rational) end proc, eq), AllSolutions, solutions = 15, tolerances = 10^(-10), number = 1500, {alpha = -2 .. 2, beta = -2 .. 2, chi = -1 .. 1, eta = -1 .. 1}, evaluationlimit = 1000000);

Warning,  computation interrupted

 

try g := proc () SolveEquations(map(proc (t) options operator, arrow; convert(t, rational) end proc, eq), AllSolutions, solutions = 7, tolerances = 1/10000000000000, number = 1000, {alpha = -2 .. 2, beta = -2 .. 2, chi = -1 .. 1, eta = -1 .. 1}, evaluationlimit = 1000000) end proc; sols := [timelimit(300, g())] catch: printf("waiting") end try

waiting

 

``

``



Download question_15.07.11.mw

@Preben Alsholm 

try           

    g:= proc()           

    solve(eq);           

end proc:          

sols:=[timelimit(300, g())];                  

catch "Error, (in fsolve/polyill) time expired" :
sols:=SolveEquations(eq);

 end try;
in my opinion,"Error, (in fsolve/polyill) time expired",the program still may run,but i meet the program stop after the messege.

@Markiyan Hirnyk

hi, the equations read as 

eq:=[2*x-0.2e-1*y-2.04*sqrt(-v^2+1)*v, 2*y-0.2e-1*x-2.16*sqrt(-u^2+1)*u, 2*u+2.16*u^2*y/sqrt(-u^2+1)-2.16*sqrt(-u^2+1)*y, 2*v+2.04*v^2*x/sqrt(-v^2+1)-2.04*sqrt(-v^2+1)*x] ;

i do as follows using DirectSearch package v.2

i find the solutions not the same,some time the results not much difference,but another,sols1 have one solution,sols2 have three solutions.in some time,some solutions are lost.may i have run the command serveral times? regards.

thanks Edgardo very much,I appreciate your early reply.Provided by Edgardo ,it's right using Maple 17.01.

thanks Edgardo very much,I appreciate your early reply.Provided by Edgardo ,it's right using Maple 17.01.

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