On the wave length of smooth periodic traveling waves of the Camassa-Holm equation

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Geyer, A.¹  Villadelprat, J.² 

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain

[2] Univ Rovira & Virgili, Dept Engn Informat & Matemat, E-43007 Tarragona, Spain

关键词: Camassa-Holm equation;    Traveling wave solution;    Wave length;    Wave height;    Center;    Critical period;   

DOI  :  10.1016/j.jde.2015.03.027

来源: Elsevier

【 摘 要 】

This paper is concerned with the wave length A 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 bar right arrow lambda(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 with the equation, which distinguish between the two possible qualitative behaviors of lambda(a), namely monotonicity and unimodality. The key point is to relate lambda(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. (C) 2015 The Authors. Published by Elsevier Inc.

【 授权许可】

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