2023/09/29 by Brett Ehrman, Ehrman, Brett, Mathew A. Johnson +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2309.17289
openalex publication_date 2023/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we identify criteria that guarantees the nonlinear orbital stability of a given periodic traveling wave solution within the b-family Camassa-Holm equation. These periodic waves exist as 3-parameter families (up to spatial translations) of smooth traveling wave solutions, and their stability criteria are expressed in terms of Jacobians of the conserved quantities with respect to these parameters. The stability criteria utilizes a general Hamiltonian structure which exists for every b>1, and hence applies outside of the completely integrable cases (b=2 and b=3).