Lumps and interaction solutions to the (4 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation in fluid mechanics
Lulu Fan, Taogetusang Bao
Abstract
In this paper, we introduce a new nonlinear evolution equation, which is ([Formula: see text])-dimensional variable-coefficient Kadomtsev–Petviashvili equation. First, according to the Hirota bilinear method, we get some exact solutions of the equation, including lump solution, lump-soliton solution, rogue-soliton solution and lump-kink solution. Then, we obtain some new exact solutions by generalizing the form of the lump solution on a further solution. Finally, based on the symbolic calculation method with Mathematica, the characteristics of the interaction solutions are shown in the graphs and we analyze the dynamic change of the solutions. Furthermore, we discuss the applications of these solutions in physics via the analysis.