The integrability of a (2+1)-dimensional nonlinear wave equation: Painlevé property, multi-order breathers, multi-order lumps and hybrid solutions

Abstract

The (2+1)-dimensional nonlinear wave equation is proposed by exchanging the x,y-spaces (x↔y) in the (2+1)-dimensional Hirota bilinear equation. A singularity structure analysis is performed for the (2+1)-dimensional nonlinear wave equation, which admits the Painlevé property. Multi-solitons of the nonlinear wave equation are obtained by solving the corresponding Hirota bilinear form. Multi-order breathers are derived by establishing the complex conjugate relations of the parameters in the multi-solitons. One-order breather can be divided to three classes based on the path of the breather. Multi-order lumps of the nonlinear wave equation are given by the long wave limit method in the multi-solitons. Lump wave localizes in all directions and decays algebraically. To get the complicated interaction solutions, some hybrid solutions including the multi-solitons, multi-order breathers and multi-order lumps are constructed. The dynamics behaviors of these hybrid solutions are analyzed both in numerical simulations and graphs ways.