Symmetric Waves are Traveling Waves for the Rotation-Camassa–Holm Equation

In this paper, we prove that classical symmetric solutions to the rotation-Camassa–Holm equation must be traveling wave solutions. We discover how the symmetric structure is connected to the steady structure of solutions to the rotation-Camassa–Holm equation, and give a straightforward proof for sym...

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Bibliographic Details
Published inJournal of mathematical fluid mechanics Vol. 23; no. 3
Main Authors Wang, Tingting, Yang, Shaojie, Han, Xuanxuan
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.08.2021
Springer Nature B.V
Subjects
Classical and Continuum Physics
Fluid mechanics
Fluid- and Aerodynamics
Mathematical Methods in Physics
Physics
Physics and Astronomy
Rotation
Theoretical mathematics
Traveling waves
Traveling waves
Symmetric solutions
The rotation-Camassa–Holm equation
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Summary:In this paper, we prove that classical symmetric solutions to the rotation-Camassa–Holm equation must be traveling wave solutions. We discover how the symmetric structure is connected to the steady structure of solutions to the rotation-Camassa–Holm equation, and give a straightforward proof for symmetric waves to be traveling waves.
ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-021-00602-1