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On solutions of the Camassa-Holm equation. (English) Zbl 1039.76006

Summary: The techniques that have been developed for the application of the inverse-scattering transform method to the solution of 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.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q53 KdV equations (Korteweg-de Vries equations)
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35K40 Second-order parabolic systems
35P25 Scattering theory for PDEs
35Q51 Soliton equations
35R30 Inverse problems for PDEs
76B25 Solitary waves for incompressible inviscid fluids

Software:

Maple; Mathematica
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