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May/June 2020 On the stable self-similar waves for the Camassa-Holm and Degasperis-Procesi equations
Liangchen Li, Hengyan Li, Weiping Yan
Adv. Differential Equations 25(5/6): 315-334 (May/June 2020).

Abstract

This paper mainly studies the explicit wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the Camassa-Holm and Degasperis-Procesi equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler's equation in the shallow water regime. We prove that the Camassa-Holm and Degasperis-Procesi equations admit stable explicit self-similar solutions. After that, the nonlinear instability of explicit self-similar solution for the Korteweg-de Vries equation is given.

Citation

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Liangchen Li. Hengyan Li. Weiping Yan. "On the stable self-similar waves for the Camassa-Holm and Degasperis-Procesi equations." Adv. Differential Equations 25 (5/6) 315 - 334, May/June 2020.

Information

Published: May/June 2020
First available in Project Euclid: 16 May 2020

zbMATH: 07243146
MathSciNet: MR4099222

Subjects:
Primary: 35A21, 35B35, 35Q35

Rights: Copyright © 2020 Khayyam Publishing, Inc.

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Vol.25 • No. 5/6 • May/June 2020
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