The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation

We consider a three-parameter family of non-linear equations with -order non-linearities. Such a family includes as a particular member the well-known b-equation, which encloses the famous Camassa-Holm equation. For certain choices of the parameters, we establish a global existence result and show a...

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Bibliographic Details
Published inApplicable analysis Vol. 102; no. 12; pp. 3209 - 3222
Main Authors Duruk Mutlubas, Nilay, Freire, Igor Leite
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 13.08.2023
Taylor & Francis Ltd
Subjects
Camassa-Holm-type equations
Cauchy problems
continuation of solutions
global existence of solution
Nonlinear equations
Parameters
Wave breaking
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Summary:We consider a three-parameter family of non-linear equations with -order non-linearities. Such a family includes as a particular member the well-known b-equation, which encloses the famous Camassa-Holm equation. For certain choices of the parameters, we establish a global existence result and show a scenario that prevents the wave breaking of solutions. Also, we explore unique continuation properties for some values of the parameters.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2022.2057304