Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation
Exactly Solvable and Integrable Systems
2013-02-06 v1
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.
Keywords
Cite
@article{arxiv.0903.3663,
title = {Explicit multipeakon solutions of Novikov's cubically nonlinear integrable Camassa-Holm type equation},
author = {Andrew N. W. Hone and Hans Lundmark and Jacek Szmigielski},
journal= {arXiv preprint arXiv:0903.3663},
year = {2013}
}
Comments
41 pages, LaTeX + AMS packages + pstricks