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. (Contact us about this Publication)|
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.
|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):