On a generalized Kadomtsev-Petviashvili equation with variable coefficients via symbolic computation

Considering the inhomogeneities of media, a generalized Kadomtsev - Petviashvili equation with time-dependent coefficients is hereby investigated with the aid of symbolic computation. The exact analytic one- and two-soliton solutions under certain constraints are obtained by employing the variable-coefficient balancing-act method and Hirota method. Based on its bilinear form, the Lax pair, auto-B cklund transformation (in both the bilinear form and the Lax pair form) and nonlinear superposition formula for such an equation are presented. Moreover, some figures are plotted to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.