Existence and analyticity of lump solutions for generalized benney-luke equations
We prove the existence and analyticity of lump solutions (finiteenergy solitary waves) for generalized Benney-Luke equations that arise in the study of the evolution of small amplitude, three-dimensional water waves. The family of generalized Benney-Luke equations reduce formally to the generalized...
- Autores:
-
Quintero, José Raúl
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2002
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/43807
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/43807
http://bdigital.unal.edu.co/33905/
- Palabra clave:
- Weakly nonlinear waves
travelling waves
concentrationcompactness
analyticity
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | We prove the existence and analyticity of lump solutions (finiteenergy solitary waves) for generalized Benney-Luke equations that arise in the study of the evolution of small amplitude, three-dimensional water waves. The family of generalized Benney-Luke equations reduce formally to the generalized Korteweg-de Vries (GKdV) equation and to the generalized Kadomtsev Petviashvili (GKP-I or GKP-II) equation in the appropriate limits. Existence lumps is proved via the concentration-compactness method. When surface tensión is sufficiently strong (Bond number larger thanlj3), we prove that a suitable family of generalized Benney-Luke lump solutions converges to a nontrivial lump solution for the GKP-I equation. |
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