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Volume 6, Number 4, 2016, Pages 907-916                                                                DOI:10.11948/2016059
Multi-peakon solutions to a four-component Camassa-Holm type system
Zhaqilao
Keywords:Peakon wave, four-component Camassa-Holm type system, integrable system.
Abstract:
      A four-component Camassa-Holm type system with cubic nonlinearity is investigated. It allows an arbitrary function $\Gamma(x,t)$ 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 $\Gamma(x,t)$. 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.
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