Wronskian and Grammian determinant structure solutions for a variable-coefficient forced Kadomtsev–Petviashvili equation in fluid dynamics

Taking the inhomogeneities of media and nonuniform boundaries into account, the variable-coefficient equations can describe more realistic physical phenomena than their constant-coefficient counterparts. In this paper, a variable-coefficient forced Kadomtsev–Petviashvili equation with inhomogeneous nonlinearity, dispersion, perturbed term and external force is investigated. Using a modified dependent variable transformation, this equation is first bilinearized. Then, the N-soliton solutions in two different kinds of determinant structure, that is the Wronskian and Grammian determinant soliton solutions for the variable-coefficient forced Kadomtsev–Petviashvili equation are presented and verified under certain coefficient constraints. The sample soliton solutions are given by choosing suitable determinant elements, and several kinds of soliton evolution situations are discussed and illustrated.