Participants : Caterina Calgaro [ correspondant ] , Jean-Paul Chehab.
We have developed a set of numerical codes, written in Matlab, to solve various 1D nonlinear wave equations (Korteweg-de-Vries, Benjamin-Ono, nonlinear Schrödinger),with or without damping term. These equations are discretized by pseudo-spectral or finite difference methods (compact schemes); a part of the corresponding study can be found in  . We compare the long time stability of various numerical methods and their capability to reproduce some physical invariants. These codes are still in development in order to simulate blow-up phenomena.