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Lookup NU author(s): Professor Robin Johnson
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The techniques that have been developed for the application of the inverse-scattering transform method to the solution of the Camassa-Holm equation, principally by Constantin, are implemented. We use this approach, first, to represent the known solitary-wave solution in a simple parametric form, and then, second, to obtain the general two- and three-soliton solutions. (These latter two solutions require rather extensive use of mathematical packages, MATHEMATICA and MAPLE, in order to complete the construction of solutions.) A number of examples are presented; the phase shifts, evident after an interaction, are found and the special limit that recovers the peakon solutions is discussed.
Author(s): Johnson RS
Publication type: Article
Publication status: Published
Journal: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Year: 2003
Volume: 459
Issue: 2035
Pages: 1687-1708
ISSN (print): 1364-5021
ISSN (electronic): 1471-2946
Publisher: Royal Society Publishing
URL: http://dx.doi.org/10.1098/rspa.2002.1078
DOI: 10.1098/rspa.2002.1078
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