@Article{JPDE-23-251,
author = {José Raúl Quintero },
title = {Solitary Water Waves for a 2D Boussinesq Type System},
journal = {Journal of Partial Differential Equations},
year = {2010},
volume = {23},
number = {3},
pages = {251--280},
abstract = {<p>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.</p>},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v23.n3.4},
url = {http://global-sci.org/intro/article_detail/jpde/5233.html}
}