Soliton molecules, asymmetric solitons and some new types of hybrid solutions in (2+1)-dimensional Sawada–Kotera model

Abstract

Soliton molecules can be formed in both theoretical and experimental situations. In this paper, a new velocity resonance is introduced, which can form soliton molecules for the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera equation. By selecting some suitable parameters for soliton molecules, the asymmetric solitons of the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera equation can be obtained. And, the interactions among multiple soliton molecules are elastic. Furthermore, some new types of hybrid solutions consisting of soliton molecules, lump wave and breather wave can be derived by utilizing velocity resonance, module resonance of wave numbers and long wave limits method. This method of solving the soliton molecules, asymmetric solitons and some new hybrid solutions can also be applied to other nonlinear evolution equations.