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Numerical comparisons of two long-wave limit models

Published online by Cambridge University Press:  15 June 2004

Stéphane Labbé  and
Lionel Paumond
Stéphane Labbé
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France. stephane.labbe@math.u-psud.fr.
Lionel Paumond
Affiliation:
Laboratoire de Mathématiques, Université Paris-Sud, Bâtiment 425, 91405 Orsay Cedex, France. stephane.labbe@math.u-psud.fr.
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Abstract

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 Equations16 (2003) 1039–1064; Pego and Quintero, Physica D132 (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.

Keywords

Benney-LukeKadomtsev-Petviashvilispectral methodlong wave limit.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 3 , May 2004 , pp. 419 - 436
Copyright
© EDP Sciences, SMAI, 2004

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