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arXiv · 2202.07110

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

Nilay Duruk Mutlubas·Igor Leite Freire
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Abstract

We consider a three-parameter family of non-linear equations with $(p+1)-$order non-linearities. Such 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 prevent the wave breaking of solutions. Also, we explore unique continuation properties for some values of the parameters.

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Nilay Duruk Mutlubas, Igor Leite Freire. 2022-02-15. The Cauchy problem and continuation of periodic solutions for a generalized Camassa-Holm equation. https://doi.org/10.1080/00036811.2022.2057304

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