An Isospectral Problem for Global Conservative Multi-Peakon Solutions of the Camassa–Holm Equation

2014/02/21 by Jonathan Eckhardt, Aleksey Kostenko · 56 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Applied mathematics #Camassa–Holm equation #Integrable system #Inverse #Inverse problem #Isospectral #Lax pair #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Peakon #math-ph #math.MP #math.SP #msc:34B07 #msc:34B09 #msc:37K10 #msc:37K15 #nlin.SI

paper · pdf · doi:10.1007/s00220-014-1905-4

published in Communications in Mathematical Physics 329(3), 893-918 (Springer Science+Business Media) · 25 pages

openalex publication_date 2014/02/21 · arxiv created 2014/06/14 · arxiv updated 2014/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce a generalized isospectral problem for global conservative multi-peakon solutions of the Camassa-Holm equation. Utilizing the solution of the indefinite moment problem given by M. G. Krein and H. Langer, we show that the conservative Camassa-Holm equation is integrable by the inverse spectral transform in the multi-peakon case.

Citations

• GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
• Global Conservative Solutions of the Camassa–Holm Equation
• Inverse Scattering Transform for the Camassa-Holm equation
• Wave breaking for nonlinear nonlocal shallow water equations
• The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations
• Sylvester's Identity and Multistep Integer-Preserving Gaussian Elimination