Solitary Water Waves for a 2D Boussinesq Type System

Solitary Water Waves for a 2D Boussinesq Type System

Year:    2010

Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 3 : pp. 251–280

Abstract

We prove the existence of solitons (finite energy solitary wave) for a Boussinesq system that arise in the study of the evolution of small amplitude long water waves including surface tension. This Boussinesq system reduces to the generalized Benney-Luke equation and to the generalized Kadomtsev-Petviashivili equation in appropriate limits. The existence of solitons follows by a variational approach involving the Mountain Pass Theorem without the Palais-Smale condition. For surface tension sufficiently strong, we show that a suitable renormalized family of solitons of this model converges to a nontrivial soliton for the generalized KP-I equation.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v23.n3.4

Journal of Partial Differential Equations, Vol. 23 (2010), Iss. 3 : pp. 251–280

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:    Weakly nonlinear waves