# 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 Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equationsQ Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equationsQ Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanicsQ Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science Andrew N W Hone 29 Jun 2011 13:54 UTC 28 May 2019 15:23 UTC https://kar.kent.ac.uk/id/eprint/24242 (The current URI for this page, for reference purposes)