Numerical comparisons of two long-wave limit models
Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France. email@example.com.
The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999) 476–496) that (BL) is linked to the Kadomtsev-Petviashvili equation for almost one-dimensional waves propagating in one direction. We study here numerically the link between (KP) and (BL) and we point out the coupling effects emerging by considering two solitary waves propagating in two opposite directions.
Mathematics Subject Classification: 35L05 / 35Q51 / 35Q53 / 65J15 / 65M70
Key words: Benney-Luke / Kadomtsev-Petviashvili / spectral method / long wave limit.
© EDP Sciences, SMAI, 2004