Bilinear Bäcklund Transformation for a Variable-Coefficient Kadomtsev–Petviashvili Equation

Resorting to the Hirota bilinear form, a bilinear Bäcklund transformation (BT) is obtained for a variable-coefficient Kadomtsev–Petviashvili equation. As applications, based on the resulting bilinear BT, single-soliton solutions and two-soliton solutions together with their soliton characteristics are presented for the equation. Furthermore, starting from the bilinear BT, a Lax pair and a new variable-coefficient (2+1)-dimensional nonlinear evolution equation is derived.