2005/04/26 by Yoshimasa Matsuno · 75 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Applied mathematics #Camassa–Holm equation #Integrable system #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Parametric equation #Parametric statistics #Peakon #Phase (matter) #Physics #Quantum mechanics #Representation (politics) #Simple (philosophy) #Soliton #Statistical physics #Statistics #nlin.SI
paper · pdf · doi:10.1143/jpsj.74.1983
published in Journal of the Physical Society of Japan 74(7), 1983-1987 (Physical Society of Japan) · 14 pages
arxiv created 2005/04/26 · openalex publication_date 2005/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The parametric representation is given to the multisoliton solution of the Camassa-Holm equation. It has a simple structure expressed in terms of determinants. The proof of the solution is carried out by an elementary theory of determinants. The large time asymptotic of the solution is derived with the formula for the phase shift. The latter reveals a new feature when compared with the one for the typical soliton solutions. The peakon limit of the phase shift is also considered, showing that it reproduces the known result. KEYWORDS: Camassa-Holm equation, soliton, peakon, parametric representation a)