Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa--Holm type equation

Hone, Andrew N.W., Lundmark, H., Szmigielski, J. (2009) Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa--Holm type equation. Dynamics of Partial Differential Equations, 6 (3). pp. 253-289. ISSN 1548-159X.

Abstract

Recently Vladimir Novikov found a new integrable analogue of the Camassa-Holm equation, admitting peaked soliton (peakon) solutions, which has nonlinear terms that are cubic, rather than quadratic. In this paper, the explicit formulas for multipeakon solutions of Novikov's cubically nonlinear equation are calculated, using the matrix Lax pair found by Hone and Wang. By a transformation of Liouville type, the associated spectral problem is related to a cubic string equation, which is dual to the cubic string that was previously found in the work of Lundmark and Szmigielski on the multipeakons of the Degasperis-Procesi equation

Item Type:	Article
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations Q Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanics Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics
Divisions:	Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User:	Andrew N W Hone
Date Deposited:	29 Jun 2011 13:54 UTC
Last Modified:	28 May 2019 15:23 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/24242 (The current URI for this page, for reference purposes)