Hone, A.N.W. and Wang, JP (2003) Prolongation algebras and Hamiltonian operators for peakon equations. Inverse Problems , 19 (1). pp. 129-145. ISSN 0266-5611.
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| Official URL http://dx.doi.org/10.1088/0266-5611/19/1/307 |
Abstract
We consider a family of non-evolutionary partial differential equations, labelled by a single parameter b, all of which admit multi-peakon solutions. For the two special integrable cases, namely the Camassa-Holm and Degasperis-Procesi equations (b = 2 and 3), we explain how their spectral problems have reciprocal links to Lax pairs for negative flows, in the Korteweg-de Vries and Kaup-Kupershmidt hierarchies respectively. An analogous construction is presented in the case of the Sawada-Kotera hierarchy, leading to a new zero-curvature representation for the integrable Vakhnenko equation. We show how the two special peakon equations are isolated via the Wahlquist-Estabrook prolongation algebra method. Using the trivector technique of Olver, we provide a proof of the Jacobi identity for the non-local Hamiltonian structures of the whole peakon family. Within this class of Hamiltonian operators (also labelled by b), we present a uniqueness theorem which picks out the special cases b = 2, 3.
| Item Type: | Article |
|---|---|
| Uncontrolled keywords: | CAMASSA-HOLM EQUATION; BACKLUND-TRANSFORMATIONS; EVOLUTION-EQUATIONS; SYMMETRY APPROACH; KDV EQUATION; SOLITONS |
| 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 18:28 |
| Last Modified: | 16 Dec 2011 11:24 |
| Resource URI: | http://kar.kent.ac.uk/id/eprint/759 (The current URI for this page, for reference purposes) |
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