On the wave length of smooth periodic traveling waves of the Camassa-Holm equation
Geyer, Anna (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Villadelprat Yagüe, Jordi (Universitat Rovira i Virgili. Departament d'Enginyeria Informàtica i Matemàtiques)

Date:	2015
Abstract:	This paper is concerned with the wave length of smooth periodic traveling wave solutions of the Camassa-Holm equation. The set of these solutions can be parametrized using the wave height a (or ''peak-to-peak amplitude''). Our main result establishes monotonicity properties of the map a (a), i. e. , the wave length as a function of the wave height. We obtain the explicit bifurcation values, in terms of the parameters associated to the equation, which distinguish between the two possible qualitative behaviours of (a), namely monotonicity and unimodality. The key point is to relate (a) to the period function of a planar differential system with a quadratic-like first integral, and to apply a criterion which bounds the number of critical periods for this type of systems.
Grants:	Ministerio de Educación y Ciencia MTM2008-03437
Note:	Agraïments: A. Geyer is supported by the FWF project J3452 "Dynamical Systems Methods in Hydrodynamics" of the Austrian Science Fund. J.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Camassa-Holm equation ; Traveling wave solution ; Wave length ; Wave height ; Center ; Critical period
Published in:	Journal of differential equations, Vol. 259 (2015) , p. 2317-2332, ISSN 1090-2732

DOI: 10.1016/j.jde.2015.03.027
PMID: 27546904

Postprint 15 p, 645.7 KB

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