|Revista Colombiana de Matemáticas|
(2002)Páginas 71 - 95
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.