In this paper, we study a (2+1)-dimensional generalized Camassa-Holm (2dgCH) equation with both quadratic and cubic nonlinearity. We derive a peaked soliton (peakon) solution, double-peakon solutions, and kink-peakon solutions. In particular, weak kink -peakon solution is the first time to address in the 2 + 1-dimensional integrable system.
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