# Question:Problem with coefficients in PDEtools

## Question: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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