Question: Two different behaviors in the same PDE..??

Greetings,

I need some help/advice because I think I am going crazy..!

I am trying to solve numerically a system of two PDE's. My initial condition is a gaussian and I apply cyclic boundaries.

With Maple 18 and pdsolve/numeric I am waiting a considerable amount of time and the result is a bell shaped travelling wave that increases its height over time. The clush between two such waves leaves them almost unaffected (the big pass through the small one).

With Mathematica 10 and NDSolve the waiting time is almost zero and the result (after few timesteps) is a shock wave travelling with steady height. Moreover, the clush between two of them is fully plastic (the big "eat" the small one)

I double-triple check the equations and the boundary conditions and I assure you that are the same..Any ideas what is hapening? Is there any way to check that the Maple results are correct?