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Cusped solitons of the Camassa-Holm equation. I. Cuspon solitary wave and antipeakon limit

Lookup NU author(s): Dr Allen Parker

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Abstract

A factorisaton method is used to obtain the cusped soliton of the Camassa-Holm equation in parametric form. It is shown how this piecewise analytic solution arises from an associated smooth solitary wave. The PQ-decomposition of the explicit solution is then used to determine the dispersionless limit (κ → 0) in which the cuspon converges to an antipeakon. The special cuspon solution reported by Kraenkel and Zenchuk [Kraenkel RA, Zenchuk A. Camassa-Holm equation: transformation to deformed sinh-Gordon equations, cuspon and soliton solutions. J Phys A: Math Gen 1999;32:4733-47] is recovered and examined in the context of the parametric representation. The cusped solitary wave of a short-wave version of the Camassa-Holm model is also deduced from the cuspon in an appropriate limit. © 2007 Elsevier Ltd. All rights reserved.

Publication metadata

Author(s): Parker A

Publication type: Article

Publication status: Published

Journal: Chaos, Solitons and Fractals

Year: 2007

Volume: 34

Issue: 3

Pages: 730-739

ISSN (print): 0960-0779

ISSN (electronic): 1873-2887

Publisher: Pergamon

URL: http://dx.doi.org/10.1016/j.chaos.2007.01.033

DOI: 10.1016/j.chaos.2007.01.033

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