Soliton solutions and their degenerations in the (2+1)-dimensional Hirota-Satsuma-Ito equations with time-dependent linear phase speed

Abstract 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.