Lump and line soliton pairs to a [formula omitted]-dimensional integrable Kadomtsev–Petviashvili equation

Abstract

By introducing the positive quadratic function, one kind of rational lump solution to a (2+1)-dimensional integrable Kadomtsev–Petviashvili (KP) equation is presented. By combining the positive quadratic function and an exponential function, we find the fusion and fission phenomena for two kinds of typical local excitations, which occur between a lump and a stripe soliton. Furthermore, by adding a hyperbolic function to the quadratic function, we have derived the solution with the interaction between a lump and line soliton pairs. The dynamical behaviors of such local solutions are discussed by choosing the appropriate parameters.