Stability of peakons for a modified Camassa-Holm equation

2013/04/15 by Xingxing Liu, Zhaoyang Yin, Liu, Xingxing +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1304.4038

openalex publication_date 2013/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the orbital stability of peakons for a modified Camassa-Holm equation with cubic nonlinearity derived from the two-dimensional Euler equation. By overcoming the difficulties caused by one of the complicated conservation laws and introducing a new auxiliary function, we prove the orbital stability of peakons for the equation.

Citations

• Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation
• Wave breaking for nonlinear nonlocal shallow water equations

Related

• Orbital stability of peakons for a generalized Camassa-Holm equation with both quadratic and cubic nonlinearity
• Stability of peakons for the generalized modified Camassa-Holm equation
• Stability of the μ-Camassa-Holm Peakons
• Instability of H¹-stable peakons in the Camassa-Holm equation
• Orbital stability of smooth solitary waves for the modified Camassa-Holm equation