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.
|76B15||Water waves, gravity waves; dispersion and scattering, nonlinear interaction|
|35Q53||KdV-like (Korteweg-de Vries) equations|
|35-04||Machine computation, programs (partial differential equations)|
|35K40||Systems of second-order parabolic equations, general|
|35P25||Scattering theory (PDE)|
|35R30||Inverse problems for PDE|
|76B25||Solitary waves (inviscid fluids)|