Advances in Differential Equations
- Adv. Differential Equations
- Volume 25, Number 5/6 (2020), 315-334.
On the stable self-similar waves for the Camassa-Holm and Degasperis-Procesi equations
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.
Adv. Differential Equations, Volume 25, Number 5/6 (2020), 315-334.
First available in Project Euclid: 16 May 2020
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Mathematical Reviews number (MathSciNet)
Li, Liangchen; Li, Hengyan; Yan, Weiping. On the stable self-similar waves for the Camassa-Holm and Degasperis-Procesi equations. Adv. Differential Equations 25 (2020), no. 5/6, 315--334. https://projecteuclid.org/euclid.ade/1589594421