A (2+1)-dimensional completely generalized Hirota-Satsuma-Ito equation is studied. Based on the Hirota bilinear method, multi-kink solutions are obtained. The higher-order lump solutions are obtained by the long-wave limit approach. By selecting the complex conjugate parameters conditions for multi-kink solutions, the multi-breather solutions are constructed. Moreover, ten kinds of interaction solutions consisted of three waves for kink, breather and lump are obtained. Some dynamical behaviors of the solutions obtained in the paper are shown by figures.
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