2012/04/20 by Shijun Liao, Liao, Shijun
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1204.4517
11 pages, 4 figures, 2 tables
arxiv created 2012/04/20 · openalex publication_date 2012/04/20 · arxiv updated 2012/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Unlike the Boussinesq, KdV and BBM equations, the celebrated Casamma-Holm (CH) equation can model both phenomena of soliton interaction and wave breaking. Especially, it has peaked solitary waves in case of omega=0. Besides, in case of omega > 0, its solitary wave "becomes C^∞ and there is no derivative discontinuity at its peak", as mentioned by Camassa and Holm in 1993 (PRL). However, it is found in this article that the CH equation has peaked solitary waves even in case of omega > 0. Especially, all of these peaked solitary waves have an unusual property: their phase speeds have nothing to do with the height of peakons or anti-peakons. Therefore, in contrast to the traditional view-points, the peaked solitary waves are a common property of the CH equation: in fact, all mainstream models of shallow water waves admit such kind of peaked solitary waves