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Conservation Laws and Web-Solutions for the Benney--Luke Equation

Authors :
Ablowitz, Mark
Curtis, Christopher
Publication Year :
2012

Abstract

A long wave multi-dimensional approximation of shallow water waves is the bi-directional Benney-Luke equation. It yields the well-known Kadomtsev-Petviashvili equation in a quasi one-directional limit. A direct perturbation method is developed; it uses the underlying conservation laws to determine the slow evolution of parameters of two space dimensional, non-decaying web-type solutions to the Benney-Luke 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 Kadomtsev-Petviashvilli and the Benney-Luke equations and are also used to obtain amplitude information regarding particular web solutions. Additional dissipative perturbations to the Benney-Luke equation are also studied.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1212.0149
Document Type :
Working Paper
Full Text :
https://doi.org/10.1098/rspa.2012.0690