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.
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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