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-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) |

35Q51 | Soliton-like equations |

35R30 | Inverse problems for PDE |

76B25 | Solitary waves (inviscid fluids) |