How can I solve coupled nonlinear hyperbolic equations?

I am trying to solve the two coupled bvp equations listed as below:

where γandρ are constants. I don't think pdepe can solve this system as I am having trouble converting it to the appropriate form that is required by pdepe.

My initial conditions can be and and my boundary condition can be

It would be great if someone can help me solve this!

Answer 1

[Torsten]

CLAWPACK available under

https://www.clawpack.org/

is an excellent solver for hyperbolic systems of differential equations.

A MATLAB solver for this kind of PDEs is not known to me.

[Devanjith Fonseka]

That's a bummer Torsten, and if you say it has to be true :(

thanks!