I am trying to reduce a nonlinear PDE with the indendent variables $(x,y,t)$ and the dependent variable $\psi(x,y,t)$. $a,b,c$ and $r$ are constants.

I want to use the following substitution:

zeta=(-ax+by)/b, gamma=(bt-x)/b, lambda(zeta,gamma)=exp(-c*exp(rt))u(x,y,t)

This is what I have tried so far:

My first approach using convert function:

restart:

with(PDETools):

declare(psi(x,y,t),lambda(zeta,gamma));

tr:={(-ax+by)/b=zeta,(bt-x)/b=gamma};

eq1:=psi->PDE-equation;

eq2:=eq1(e^{ce^{rt}}*lambda((-ax+by)/b,(bt-x)/b);

eq3:=convert(algsubs(tr,eq2),diff);

This gives me an error: "Error, invalid input: algsubs expects its 1st argument, p, to be of type algebraic = algebaric, but received{(t*u[infintity]-x)/u[infinity]=gamma,....}"

Another approach using dchange:

restart:

with(PDETools):

declare(psi(x,y,t),lambda(zeta,gamma));

eq1:=0=PDE-equation;

tr1:={zeta=(-ax+by)/b,gamma=(bt-x)/b,lambda(zeta,gamma)=-e^{ce^{rt}}*psi(x,y,t)};

tr2:=sove(tr1,{x,y,t,psi(x,y,t)});

eq2:=dchange(tr2,eq1,[zeta,gamma,lambda(zeta,gamma)]);

Here I get the error: "Error, (in dchange/info) found {t} in both lhs and rhs of ´1st. set´ of transformation equations.