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A new integrable equation with peakon solutions

Degasperis, A., Holm, Darryl D., Hone, Andrew N.W. (2002) A new integrable equation with peakon solutions. Theoretical and Mathematical Physics, 133 (2). pp. 1463-1474. ISSN 0040-5779. (doi:10.1023/A:1021186408422) (KAR id:684)

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http://dx.doi.org/10.1023/A:1021186408422

Abstract

We consider a new partial differential equation recently obtained by Degasperis and Procesi using the method of asymptotic integrability; this equation has a form similar to the Camassa-Holm shallow water wave equation. We prove the exact integrability of the new equation by constructing its Lax pair and explain its relation to 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 as a superposition of multipeakons, and we describe the integrable finite-dimensional peakon dynamics and compare it with the analogous results for Camassa-Holm peakons.

Item Type: Article
DOI/Identification number: 10.1023/A:1021186408422
Uncontrolled keywords: peakons; reciprocal transformations; weak solutions
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Andrew Hone
Date Deposited: 19 Dec 2007 18:25 UTC
Last Modified: 06 Feb 2020 04:00 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/684 (The current URI for this page, for reference purposes)
Hone, Andrew N.W.: https://orcid.org/0000-0001-9780-7369
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