A new method of generating the lump molecules and localized interaction solutions to the (2+1)-dimensional SK equation

Abstract

The (2+1)-dimensional Sawada-Kotera (SK) equation is an important integrable model, which has wide applications in rivers, lakes, atmosphere, the conformal field and quantum gravity gauge field. In this paper, we introduce a new method for constructing the lump molecules in the SK equation. Then, by using this method and imposing the complexification restrictions, velocity resonant principle, we obtain some hybrid wave solutions, which include the interactions between a lump molecule and two separated solitons, between a lump-lump-soliton molecule and a single soliton, between a lump molecule and a soliton molecule, between a lump molecule and a breather, as well as the lump-lump-breather molecule. Dynamical behaviors of these solutions are analyzed theoretically and graphically. The method introduced can be effectively used to study the wave solutions of other nonlinear PDEs. The results obtained not only enrich the types of soliton molecules, but also can be helpful in the study of the propagation behaviors of nonlinear waves.