Hello everyone!
Could you help me with the next problem:

1. I have a nonlinear pde system(two equations, two unknown functions: tau(t, r) & R(t, r)) of hyperbolic type.

2. And I have no idea how to solve it.

3. But I know some interesting things about it:

• In direct variables (tau(t, r) & R(t, r)) this is a nonlinear system maple2.mw
• But in inverse variables (t(tau, R) & r(tau, R)) it splits into two independent linear differential equations.maple3.mw And we can get a solutions of each in HeunC functions(it would be great if maple could give me an inverse Heun's functions, I couldn't find how). 

4(last). I have a condition in which one of two equtaions = 0, (this condition: tau(t, r) = t) and now I want to try to see what one of the unknown functions(R(t, r)) looks like. But I can not use numeric values. The system describes a spherical gravitational wave, depends on time and distance. r > mass so i want to see some discrete solutions of R(t, r)(jpeg file).the dimensions of t and r are the same. Maybe you have some ideas?