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) | ||
|
Download (1087Kb)
|
![[img]](http://kar.kent.ac.uk/style/images/fileicons/application_pdf.png)
|
|
| Official URL 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 |
|---|---|
| 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) |
- Depositors only (login required):
