New mixed solutions generated by velocity resonance in the $$(2+1)$$-dimensional Sawada–Kotera equation

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