Traveling surface waves of moderate amplitude in shallow water
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Geyer, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2014
Abstract:	We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of elevation and depression, including a family of solitary waves with compact support, where the amplitude may increase or decrease with respect to the wave speed. Our approach is based on techniques from dynamical systems and relies on a reformulation of the evolution equation as an autonomous Hamiltonian system which facilitates an explicit expression for bounded orbits in the phase plane to establish existence of the corresponding periodic and solitary traveling wave solutions.
Grants:	Ministerio de Ciencia e Innovación MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: The second author is supported by the FWF project J3452 "Dynamical Systems Methods in Hydrodynamics" of the Austrian Science Fund.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Compact support ; Homoclinic orbit ; Shallow water ; Solitary waves
Published in:	Nonlinear Analysis : Theory, Methods and Applications, Núm. 102 (2014) , p. 105-119, ISSN 0362-546X

DOI: 10.1016/j.na.2014.02.005
PMID: 24895474

Postprint 21 p, 469.1 KB

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