Exact Solutions for a Nonisospectral and Variable-Coefficient Kadomtsev--Petviashvili Equation

The bilinear form for a nonisospectral and variable-coefficient Kadomtsev--Petviashvili equation is obtained and some exact soliton solutions are derived by the Hirota method and Wronskian technique. We also derive the bilinear Bäcklund transformation from its Lax pairs and find solutions with the help of the obtained bilinear Bäcklund transformation.