Numerical behaviour of stable and unstable solitary waves

In this paper we analyse the behaviour in time of the numerical approximations to solitary wave solutions of the generalized Benjarnin-Bona-Mahony equation. This equation possesses an important property: the stability of these solutions depends on their velocity. We identify the error propagation mechanisms in both the stable and unstable case. In particular, we show that in the stable case, numerical methods that preserve some conserved quantities of the problem are more appropriate for the simulation of this kind of solutions. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.