Some Exact Solutions to Generalized Kadomtsev-Petviashvili Equation

Abstract

Most of the papers have explored the interactions between solitons with a zero background, while reports about exact solutions for nonzero background are rare. Hence, this paper is aimed at exploring the breather, lump, and interaction solutions with a small perturbation to ( 2 + 1 )-dimensional generalized Kadomtsev-Petviashvili (gKP) equation. General high-order periodic breather solutions are obtained using Hirota’s bilinear method with a small perturbation. At the same time, combining the use of long wave limit methods and module resonance constraints, general lump solutions and mixed solutions to gKP equation are generated. Finally, the space-time structures of the breather solutions, lump solutions, and interaction solutions are investigated and discussed.