TY - JOUR
T1 - Solitary Water Waves for a 2D Boussinesq Type System
JO - Journal of Partial Differential Equations
VL - 3
SP - 251
EP - 280
PY - 2010
DA - 2010/08
SN - 23
DO - http://doi.org/10.4208/jpde.v23.n3.4
UR - https://global-sci.org/intro/article_detail/jpde/5233.html
KW - Weakly nonlinear waves
KW - solitary waves (solitons)
KW - Mountain Pass theorem
AB - <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>