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Sociedad Colombiana de Matemáticas:Publicaciones

Revista Colombiana de Matemáticas

Volumen 36 [2] (2002)Páginas 71 - 95

Existence and analyticity of lump solutions for generalized Benney-Luke equations

José Raúl Quintero
Universidad del Valle, Cali COLOMBIA

Abstract. We prove the existence and analyticity of lump solutions (finite-energy 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 general- ized 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 ten- sion is sufficiently strong (Bond number larger than1/3), we prove that a suit- able family of generalized Benney-Luke lump solutions converges to a nontrivial lump solution for the GKP-I equation.

Palabras claves. Weakly nonlinear waves, travelling waves, concentration-compactness, analyticity.

Codigo AMS. 2000 Mathematics Subject Classification. Primary: 35K40. Secondary: 35B99, 35Q53.

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