Investigation of exact solutions to the (2+1)-dimensional Sakovich equation with time dependent coefficients using analytical methods

Abstract In this paper, the exact solutions of the (2 + 1)-dimensional variable coefficient Sakovich equation are investigated. Four distinct analytical methods, containing the unified method, the modified Kudryashov method, the modified G ′ G 2 -expansion method and the improved Riccati sub-equation method, are implemented to find new exact solutions of this equation. Soliton and periodic soliton solutions, elliptic solutions, kink solutions and traveling wave solutions, which are expressed in polynomial, rational, trigonometric and hyperbolic forms, have been obtained and are graphically represented with the aim of exhibiting the structures and dynamic behaviors of the equation. Furthermore, we have discussed the influence of variable coefficients on soliton behaviors in detail.