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)
Fecha: |
2015 |
Resumen: |
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. |
Ayudas: |
Ministerio de Educación y Ciencia MTM2008-03437
|
Nota: |
Agraïments: A. Geyer is supported by the FWF project J3452 "Dynamical Systems Methods in Hydrodynamics" of the Austrian Science Fund. J. |
Derechos: |
Tots els drets reservats. |
Lengua: |
Anglès |
Documento: |
Article ; recerca ; Versió acceptada per publicar |
Materia: |
Camassa-Holm equation ;
Traveling wave solution ;
Wave length ;
Wave height ;
Center ;
Critical period |
Publicado en: |
Journal of differential equations, Vol. 259 (2015) , p. 2317-2332, ISSN 1090-2732 |
DOI: 10.1016/j.jde.2015.03.027
PMID: 27546904
El registro aparece en las colecciones:
Documentos de investigación >
Documentos de los grupos de investigación de la UAB >
Centros y grupos de investigación (producción científica) >
Ciencias >
GSD (Grupo de sistemas dinámicos)Artículos >
Artículos de investigaciónArtículos >
Artículos publicados
Registro creado el 2016-01-12, última modificación el 2022-03-26