Geodesic
Numerical comparisons of two long-wave limit models
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 3, pp. 419-436

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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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     author = {Labb\'e, St\'ephane and Paumond, Lionel},
     title = {Numerical comparisons of two long-wave limit models},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {419--436},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {3},
     year = {2004},
     doi = {10.1051/m2an:2004020},
     mrnumber = {2075753},
     zbl = {1130.76324},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004020/}
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Labbé, Stéphane; Paumond, Lionel. Numerical comparisons of two long-wave limit models. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 3, pp. 419-436. doi: 10.1051/m2an:2004020

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