General $${\varvec{M}}$$-lump, high-order breather and localized interaction solutions to the $$\varvec{2+1}$$-dimensional Sawada–Kotera equation

Abstract

The $$2+1$$ -dimensional Sawada–Kotera equation is an important physical model. Here, by taking a long limit and restricting a conjugation condition to the related solitons, the general M-lump, high-order breather and localized interaction hybrid solutions are constructed, correspondingly. In order to study the dynamical behaviors, numerical simulations are implemented, which show that the parameters selected have great impacts on the types, dynamical behaviors and propagation properties of the solutions. The method proposed can be effectively applied to construct M-lumps, high-order breathers and interaction solutions of many nonlinear equations. The results obtained can be used to study the propagation phenomena of other nonlinear localized waves.