New Mixed Solutions Generated By Velocity Resonance In The (2+1)-Dimensional Sawada-Kotera Equation

Abstract Based on the mixed solutions of the (2+1)-dimensional Sawada-Kotera equation, the collisions among lump waves, line waves, and breather waves are studied in this paper. By introducing new constraints, the lump wave does not collide with other waves forever. Under the condition of velocity resonance, the soliton molecules consisting of a lump wave, a line wave and any number of breather waves are derived for the first time. In particular, the interaction of a line wave and a breather wave will generate two breathers under certain conditions, which is very interesting. Additionally, the method can also be extended to other (2+1)-dimensional integrable equations.