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Wave dynamics for peaked solitons of the Camassa-Holm equation

Lookup NU author(s): Dr Allen Parker

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Abstract

A detailed investigation of the wave dynamics for multiply peaked solitons of the Camassa-Holm equation is presented. The analysis proceeds in terms of the underlying component "peakons" using entirely elementary methods. The two-wave interactions exhibit intricate and subtle features such as role reversal, soliton absorption and annihilation, wave steepening and monodirectional propagation (for finite time) and a critical (amplitude) ratio. The discussion covers the entirety of these waveforms comprising two-peakon, peakon-antipeakon and two-antipeakon solutions. Their properties transfer to multipeakon dynamics and examples of three-wave interactions are given. © 2007 Elsevier Ltd. All rights reserved.

Publication metadata

Author(s): Parker A

Publication type: Article

Publication status: Published

Journal: Chaos, Solitons and Fractals

Year: 2008

Volume: 35

Issue: 2

Pages: 220-237

ISSN (print): 0960-0779

ISSN (electronic): 1873-2887

Publisher: Pergamon

URL: http://dx.doi.org/10.1016/j.chaos.2007.07.049

DOI: 10.1016/j.chaos.2007.07.049

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