The mixed solutions and nonlinear wave transitions for the (2 + 1)-dimensional Sawada-Kotera equation

Abstract

In this paper, we will obtain the mixed solutions of the -dimensional Sawada-Kotera equation by the Hirota bilinear method and the long wave limit method. Through applying the long wave limit method to the N-soliton solutions, we will obtain the corresponding lump solutions. Besides, we will get the mixed solutions of lump, breather and soliton solutions. Under the transition condition, we will obtain different types of nonlinear waves which include quasi-anti-dark soliton, multi-peak soliton, M-shaped soliton, quasi-periodic soliton and W-shaped soliton from the breath wave and the lump solutions. In particular, we will derive the inelastic collision modes, the elastic collision modes and the collision-free modes under specific conditions. Finally, we will display the mixed solutions and the nonlinear waves through illustrations.