MULTI-PEAKON SOLUTIONS TO A FOUR-COMPONENT CAMASSA-HOLM TYPE SYSTEM

A four-component Camassa-Holm type system with cubic nonlinearity is investigated. It allows an arbitrary function Γ(x, t) to be involved in to include some existing integrable peakon equations as special reductions. We obtain N-peakon solutions of the four-component Camassa-Holm type system with two special cases of Γ(x, t). In particular, we give one-and two-peakon solutions in an explicit formula and are graphically plotted. Further, some interesting peaked solutions are found:some peakon waves possessing positive and negative amplitudes while others decaying and growing amplitudes.