Prolongation algebras and Hamiltonian operators for peakon equations

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. (The full text of this publication is not available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication)
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)
  • Depositors only (login required):