Integrable peakon equations with cubic nonlinearity

Hone, A.N.W. and Wang, J.P. (2008) Integrable peakon equations with cubic nonlinearity. Journal of Physics A: Mathematical and Theoretical, 41 (37 (ar). ISSN 1751-8113. (Full text available)

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http://dx.doi.org/10.1088/1751-8113/41/37/372002

Abstract

We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao.

Item Type: Article
Uncontrolled keywords: Exactly Solvable and Integrable Systems (nlin.SI); Pattern Formation and Solitons (nlin.PS)
Subjects: Q Science
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Jane Griffiths
Date Deposited: 20 Apr 2009 14:30
Last Modified: 16 Dec 2011 11:23
Resource URI: http://kar.kent.ac.uk/id/eprint/15691 (The current URI for this page, for reference purposes)
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