document: 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 Benjamin-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
doc_bio_tags: B I O O O B I I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: numerical behaviour unstable solitary waves numerical approximations error propagation mechanisms numerical methods
abstractive_keyphrases: generalized benjamin-bona-mahony equation stable solitary waves