2015/11/10 by Qiaoyi Hu, Hu, Qiaoyi, Zhijun Qiao +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1511.03325
openalex publication_date 2015/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study a generalized Camassa-Holm (gCH) model with both dissipation and dispersion, which has (N + 1)-order nonlinearities and includes the following three integrable equations: the Camassa-Holm, the Degasperis-Procesi, and the Novikov equations, as its reductions. We first present the local well-posedness and a precise blow-up scenario of the Cauchy problem for the gCH equation. Then we provide several sufficient conditions that guarantee the global existence of the strong solutions to the gCH equation. Finally, we investigate the propagation speed for the gCH equation when the initial data is compactly supported.