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On solutions of the Camassa-Holm equation

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.

Publication metadata

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


DOI: 10.1098/rspa.2002.1078


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