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

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

2009-03-21

arxiv.org/abs/0903.3663v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

41 pages, LaTeX + AMS packages + pstricks

Scientific paper

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.

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