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Lookup NU author(s): Dr Allen Parker
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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.
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
URL: http://dx.doi.org/10.1016/j.chaos.2008.06.023
DOI: 10.1016/j.chaos.2008.06.023
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