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Volume 23, Issue 3
Solitary Water Waves for a 2D Boussinesq Type System

José Raúl Quintero

DOI: 10.4208/jpde.v23.n3.4

J. Part. Diff. Eq., 23 (2010), pp. 251-280.

Published online: 2010-08

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  • 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.

  • Keywords

Weakly nonlinear waves solitary waves (solitons) Mountain Pass theorem

  • AMS Subject Headings

35Q53 76B25 76D33

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v23.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/5233.html} }
TY - JOUR T1 - Solitary Water Waves for a 2D Boussinesq Type System AU - José Raúl Quintero 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 -

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.

José Raúl Quintero . (2010). Solitary Water Waves for a 2D Boussinesq Type System. Journal of Partial Differential Equations. 23 (3). 251-280. doi:10.4208/jpde.v23.n3.4
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