Toggle Main Menu Toggle Search

Open Access padlockePrints

Cusped solitons of the Camassa-Holm equation. II. Binary cuspon-soliton interactions

Lookup NU author(s): Dr Allen Parker


Full text for this publication is not currently held within this repository. Alternative links are provided below where available.


This paper extends the results of a previous work [Parker A. Cusped solitons of the Camassa–Holm equation. I. Cuspon solitary wave and antipeakon limit. Chaos, Solitons & Fractals 2007;34:730–9]—designated I—in which the solitary cuspon solution of the Camassa–Holm equation and its antipeakon limit were considered. Here, explicit binary cuspon–soliton solutions are obtained in parametric form by exploiting the factorisation procedure that was used in I. The structure and dynamics of these two-wave interactions are investigated and some unanswered questions concerning the waveforms are addressed. In particular, it is shown that, while a cuspon may be ‘swallowed-up’ by a soliton, the converse is never possible regardless of the depth of the cuspon trough. Formulae for the characteristic post-collision phase shifts are obtained and analysed in detail; this permits a reassessment of the previously reported results. Examples of twin-cusped and mixed cuspon–soliton solutions are presented within the different parameter regimes. Coincidentally, we find new two-soliton solutions of the related associated-Camassa–Holm equation. These describe binary interactions of classically smooth elevated solitons and solitary-wave troughs.

Publication metadata

Author(s): Parker A

Publication type: Article

Publication status: Published

Journal: Chaos, Solitons and Fractals

Year: 2009

Volume: 41

Issue: 3

Pages: 1531-1549

ISSN (print): 0960-0779

ISSN (electronic): 1873-2887

Publisher: Pergamon


DOI: 10.1016/j.chaos.2008.06.023


Altmetrics provided by Altmetric