Periodic wave patterns of two-dimensional Boussinesq systems |
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| Affiliation: | 1. Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA;2. Institut Universitaire de France, INLN UMR 6618 CNRS-UNSA, 1361, route des Lucioles, 06560 Valbonne, France;1. Univ. Nice Sophia Antipolis, CNRS, Labo. J.-A. Dieudonné, UMR 7351, Parc Valrose, F-06108 Nice, France;2. Inria, Sophia Antipolis Méditerranée Research Centre, Project COFFEE, France;3. Inria, Sophia Antipolis Méditerranée Research Centre, Project CASTOR, France;1. Departamento de Matemáticas, Universidad de Cádiz, PO Box 40, 11510 Puerto Real, Cádiz, Spain;2. Dipartimento di Matematica e Informatica, Università di Catania, Viale A. Doria 6, 95125 Catania, Italy;1. School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, PR China;2. School of Business Informatics and Mathematics, University of Mannheim, Mannheim 68161, Germany;3. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, PR China;1. Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France;2. Biology Department, A. Mira Bejaia University, Targa Ouzemour 06000 Bejaia, Algeria;1. Johann Radon Institute of Computational and Applied Mathematics (RICAM), Altenbergerstrasse 69, 4040 Linz, Austria;2. Computational Science Center, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria;3. Department of Mathematics, University of Central Florida, Orlando, 32816 FL, USA |
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| Abstract: | We prove the existence of a large family of two-dimensional travelling wave patterns for a Boussinesq system which describes three-dimensional water waves. This model equation results from full Euler equations in assuming that the depth of the fluid layer is small with respect to the horizontal wave length, and that the flow is potential, with a free surface without surface tension. Our proof uses the Lyapunov–Schmidt method which may be managed here, contrary to the case of gravity waves with full Euler equations. Our results are in a good qualitative agreement with experimental results. |
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