After spending a lot of time in the library, google and reading, I have narrowed down my scope of research for this system of equations that I have to solve. First, I discovered that the system is not purely nonlinear, but it is quasilinear, since the derivatives come into a linear way (although their coefficients are nonlinear). Second, there is a method for reducing PDEs to ODEs, namely th emethod od characteristics which seems to be working well for first order systems. However I have failed so far to apply it to my case since I get some trivial answers - I'm not experienced enough to handle it.
The battle is not over though: I got 3 more books plus I contacted a prof in our math department plus I emailed some guys at Caltech that seem to be working on these problems, and when I get to talk to them I'm sure they will help me a lot.
Meanwhile I have to prepare within a couple of days meterial for the introduction to EE class that I will be TAing, namely on Quantum Mechanics, Lasers and Computer Networks. A long weekend lies ahead, mon amies.
