I gave up on the parabolic equation. Anyway I created simple system for waves animation (I mean sea waves), and I found that it behaves well and that sound speed profile can be easily used with it. It has many problems and it's not suited well for sound simulation, but I could demonstrate few things. Check this out.
These shows sound propagation in sound channel with both bottom and surface reflection (in fact all borders reflects the sound, the right just a bit since the sound is weak there - it's one of the problems of this method, all borders reflects at 100%).
Frequencies are 4,8,16,32 and 64 pixels (size of the simulation is 100x500 pixels). SSP is very strong sound channel with axis exactly in center of the picture. It's completely out of scale, but it's wave-based sound propagation model and it shows how frequency affects things.
This actually animates the waves from the source, so you can see front-face moving through the medium and slowly (very) carving the shapes.
Anyway the best thing about this is I understand waves bit better now and I'm getting closer to understanding that darned parabolic equation
