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Zbl 1051.35045
Quintero, José Raúl
Existence and analyticity of lump solutions for generalized Benney-Luke equations. (English)
[J] Rev. Colomb. Mat. 36, No. 2, 71-95 (2002). ISSN 0034-7426

Summary: 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 generalized Korteweg-de Vries (GKdV) equation and to the generalized Kadomtsev-Petviashvili (GKP-I or GKP-II) equation in the appropriate limits. Existence lumps are proved via the concentration-compactness method. When surface tension is sufficiently strong (Bond number larger than 1/3), we prove that a suitable family of generalized Benney-Luke lump solutions converges to a nontrivial lump solution for the GKP-I equation.

MSC 2000:: *35L75 Nonlinear hyperbolic PDE of higher $(>2)$ order
35Q53 KdV-like equations
35Q51 Solitons

Keywords: finite-energy solitary waves; weakly nonlinear waves; travelling waves; small amplitude; three-dimensional water waves; concentration-compactness method

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