## 60 Reputation

8 years, 138 days

## Incomplete results when using 'pdsolve' ...

Maple

I tried to solve some linear differential equations,

but the result is incomplete.

The complete solutions have been derived by hand.

How can I get the right result using maple?

The example is from determining symmetres of differential equations.

Thank you!

## A problem about the "Infinitesimals" in ...

Maple

There is an example in the help of maple, that is to solve the symmetries of the equation ut=uxx using the order "Infinitesimals".

But the result i can't understand.

I solved by hand and find  _eta[u](x, t, u)=cu+b(x,t), where b(x,t) is a solution of the ut=uxx.

While in maple, b is only two exponential function which are also the solution of ut=uxx.

why?

## How do I determine the symmetries of a d...

Maple

I know there is some code to compute the symmetry of pde, but i want to compute the symmetry of some differential expression, as f(x,t,ux,ut).

The difference is that when solve the infinitesimal, we don't have the identity f(x,t,ux,ut)=0, we just take each variable in the jet space as independent.

Is there any package to do that?

help and thanks!

## How to simplify results of pdsolve?...

Maple 18

i use the pdsolve to find the solutions of a system of partial differential equations,

but the result contains some indefinite integrals, how to simplify it further?

thank you

code:

eq1 := {6*(diff(_xi[t](x, t, u), u))-3*(diff(_xi[x](x, t, u), u)), 12*(diff(_xi[t](x, t, u), u, u))-6*(diff(_xi[x](x, t, u), u, u)), 2*(diff(_xi[t](x, t, u), u, u, u))-(diff(_xi[x](x, t, u), u, u, u)), diff(_eta[u](x, t, u), t)+diff(_eta[u](x, t, u), x, x, x)+(diff(_eta[u](x, t, u), x))*u, 18*(diff(_xi[t](x, t, u), x, u))+3*(diff(_eta[u](x, t, u), u, u))-9*(diff(_xi[x](x, t, u), x, u)), 6*(diff(_xi[t](x, t, u), x, x))+3*(diff(_eta[u](x, t, u), x, u))-3*(diff(_xi[x](x, t, u), x, x)), 6*(diff(_xi[t](x, t, u), x, u, u))+diff(_eta[u](x, t, u), u, u, u)-3*(diff(_xi[x](x, t, u), x, u, u)), 12*(diff(_xi[t](x, t, u), u))-6*(diff(_xi[x](x, t, u), u))+6*(diff(_xi[t](x, t, u), x, x, u))-6*(diff(_xi[t](x, t, u), u))*u+3*u*(diff(_xi[x](x, t, u), u))-3*(diff(_xi[x](x, t, u), x, x, u))+3*(diff(_eta[u](x, t, u), x, u, u)), 12*(diff(_xi[t](x, t, u), x))-6*(diff(_xi[x](x, t, u), x))+2*(diff(_xi[t](x, t, u), t))+2*(diff(_xi[t](x, t, u), x, x, x))-4*(diff(_xi[t](x, t, u), x))*u+2*(diff(_xi[x](x, t, u), x))*u+_eta[u](x, t, u)-(diff(_xi[x](x, t, u), t))+3*(diff(_eta[u](x, t, u), x, x, u))-(diff(_xi[x](x, t, u), x, x, x))};

simplify(pdsolve(eq1))

## Problem with coefficients in PDEtools...

Maple 18

hi,

i want to compute the determining PDE system satisfied by the infinitesimals, such as the KdV equation.

but i have a problem, if i use the command

DeterminingPDE(PDE1, integrabilityconditions = false, split = false)

i can get the coefficients of independent objects, but u[t] exists.

i want to replace u[t] by (-u[x]u-u[x,x,x]), then extract the coefficients.

but i can't collect the coefficients.

my code:

with(PDEtools, DeterminingPDE, declare, diff_table, casesplit, InfinitesimalGenerator, Infinitesimals, SymmetryTest, ReducedForm, FromJet, ToJet);

declare(u(x, t));

U := diff_table(u(x, t));

PDE1 := U[]*U[x]+U[t]+U[x, x, x] = 0;

DetSys := DeterminingPDE(PDE1, integrabilityconditions = false, split = false);
detsys := FromJet(DetSys, u(x, t), differentiationnotation = diff);
pd1 := subs(U[t] = -U[]*U[x]-U[x, x, x], detsys); #u[t]->(-u[x]u-u[x,x,x])
pd2 := ToJet(pd1, [u(x, t)]);

how do i collect the coefficients?

help!

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