no. 3
Numerical comparisons of two long-wave limit models
ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 3, pp. 419-436

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.

DOI : 10.1051/m2an:2004020
Classification : 35L05, 35Q51, 35Q53, 65J15, 65M70
Keywords: Benney-Luke, Kadomtsev-Petviashvili, spectral method, long wave limit 
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     title = {Numerical comparisons of two long-wave limit models},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {419--436},
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     publisher = {EDP Sciences},
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Labbé, Stéphane; Paumond, Lionel. Numerical comparisons of two long-wave limit models. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 3, pp. 419-436. doi: 10.1051/m2an:2004020

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