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In this paper, the (2[Formula: see text]+[Formula: see text]1)-dimensional CDGKS equation is studied and its diverse soliton solutions consisting of line soliton, periodic soliton and lump soliton with different parameters are derived based on the Hirota bilinear method and long-wave limit method. Based on exact solution formulae with different parameters, the interaction between line soliton and periodic soliton, the interaction between line soliton and lump soliton, as well as the interaction between periodic soliton and lump soliton are illustrated. According to the dynamical behaviors, it can be found that the effects of different parameters are on the propagation direction and shapes. Novel soliton interaction phenomena are also observed.

This paper focuses on the exact soliton solutions of the (2+1)-dimensional generalized Hirota-Satsuma-Ito equations with time-dependent linear phase speed. Based on the Painlevé integrability test of this equation, the condition of the integrability is determined. Then the general N-soliton solutions are constructed by Hirota bilinear method. Not only the expressions of exact solutions and their degenerations, but also the spatial structures are presented for different choices of the parameters, including the line soliton, periodic soliton, lump soliton and their interaction forms.

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