The Integrability and Several Localized Wave Solutions of a Generalized (2+1)-Dimensional Nonlinear Wave Equation

This paper mainly studies the integrability and localized wave solutions of a (2+1)-dimensional nonlinear wave equation. The bilinear form, Bäcklund transformation (BT), Lax pair and infinite conservation laws of this equation can be obtained by using Bell polynomials. The localized wave solutions including lump solutions, breather solutions and interaction solutions can be presented through Hirota’s bilinear method and the ansatz method. In addition, based on mixed lump-stripe soliton solutions and mixed rogue wave-stripe soliton solutions, the fission and fusion phenomena among the lump, the single stripe soliton and the double stripe solitons are discovered. The dynamical behaviors of these localized wave solutions are analyzed by numerical simulations. These investigated solutions can enrich the study of theory for the nonlinear localized waves and are useful for the study on interaction behaviors of nonlinear waves in nonlinear optics, shallow water and oceanography.