Conservation laws and non-decaying solutions for the Benney-Luke equation

A long wave multi-dimensional approximation of shallow-water waves is the bi-directional Benney-Luke (BL) equation. It yields the well-known Kadomtsev-Petviashvili (KP) equation in a quasi one-directional limit. A direct perturbation method is developed; it uses underlying conservation laws to deter...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2013-04, Vol.469 (2152), p.20120690-20120690
Main Authors: Ablowitz, Mark J., Curtis, Christopher W.
Format: Article
Language:English
Subjects:
Approximation
Asymptotics
Benney-Luke Equation
Computer simulation
Conservation Laws
Dissipation
Evolution
Kadomtsev-Petviashvili Equation
Mathematical analysis
Mathematical models
Nonlinear Waves
Perturbation methods
Web Solutions
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Summary:A long wave multi-dimensional approximation of shallow-water waves is the bi-directional Benney-Luke (BL) equation. It yields the well-known Kadomtsev-Petviashvili (KP) equation in a quasi one-directional limit. A direct perturbation method is developed; it uses underlying conservation laws to determine the slow evolution of parameters of two space-dimensional, non-decaying solutions to the BL equation. These non-decaying solutions are perturbations of recently studied web solutions of the KP equation. New numerical simulations, based on windowing methods which are effective for non-decaying data, are presented. These simulations support the analytical results and elucidate the relationship between the KP and the BL equations and are also used to obtain amplitude information regarding particular web solutions. Additional dissipative perturbations to the BL equation are also studied.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2012.0690