Existence and analyticity of lump solutions for generalized benney-luke equations

Abstract

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.