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