Degasperis, A. and Holm, D.D. and Hone, A.N.W. (2002) A new integrable equation with peakon solutions. Theoretical and Mathematical Physics, 133 (2). pp. 1463-1474. ISSN 0040-5779.
|PDF (New Integrable Equation)|
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.
|Uncontrolled keywords:||peakons; reciprocal transformations; weak solutions|
|Subjects:||Q Science > QA Mathematics (inc Computing science)|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Judith Broom|
|Date Deposited:||19 Dec 2007 18:25|
|Last Modified:||25 Jun 2012 11:48|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/684 (The current URI for this page, for reference purposes)|
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