A New Integrable Equation with Peakon Solutions

2002/05/12 by A. Degasperis, Darryl D. Holm, D. D. Holm +5 · 5 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #nlin.CD #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0205023

14 pages, 2 figures -- to appear in NEEDS 2001 Proceedings

arxiv created 2002/05/12 · arxiv updated 2009/11/30

Abstract

We consider a new partial differential equation, of a similar form to the Camassa-Holm shallow water wave equation, which was recently obtained by Degasperis and Procesi using the method of asymptotic integrability. We prove the exact integrability of the new equation by constructing its Lax pair, and we explain its connection with a negative flow in the Kaup-Kupershmidt hierarchy via a reciprocal transformation. The infinite sequence of conserved quantities is derived together with a proposed bi-Hamiltonian structure. The equation admits exact solutions in the form of a superposition of multi-peakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa-Holm peakons.

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