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On the wave length of smooth periodic traveling waves of the Camassa-Holm equation
Geyer, Anna
Villadelprat, Jordi

Data: 2015
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
Publicat a: Journal of Differential Equations, Vol. 259 (2015) , p. 2317-2332

DOI: 10.1016/j.jde.2015.03.027

15 p, 645.7 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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 Registre creat el 2016-01-12, darrera modificació el 2016-10-06

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