# Numerical comparisons of two long-wave limit models

Stéphane Labbé; Lionel Paumond

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 3, page 419-436
- ISSN: 0764-583X

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topLabbé, Stéphane, and Paumond, Lionel. "Numerical comparisons of two long-wave limit models." ESAIM: Mathematical Modelling and Numerical Analysis 38.3 (2010): 419-436. <http://eudml.org/doc/194221>.

@article{Labbé2010,

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.
},

author = {Labbé, Stéphane, Paumond, Lionel},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Benney-Luke; Kadomtsev-Petviashvili; spectral method; long wave limit.},

language = {eng},

month = {3},

number = {3},

pages = {419-436},

publisher = {EDP Sciences},

title = {Numerical comparisons of two long-wave limit models},

url = {http://eudml.org/doc/194221},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Labbé, Stéphane

AU - Paumond, Lionel

TI - Numerical comparisons of two long-wave limit models

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 3

SP - 419

EP - 436

AB -
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.

LA - eng

KW - Benney-Luke; Kadomtsev-Petviashvili; spectral method; long wave limit.

UR - http://eudml.org/doc/194221

ER -

## References

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