Fission and Fusion Solutions to the (2+1)-Dimensional Generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt Equation Arising in Fluid Mechanics and Plasma Physics

Fission and fusion are common phenomena in nature, they usually occur in physical and biological fields. In this paper, we will give new constraint to obtain fission and fusion solutions which have the shape of the letter Y . In combination with velocity resonance method, mode resonance method and long-wave limit method, we construct the interaction solutions of y-type molecules with soliton molecules, breather molecules and lump molecules respectively. We also obtain a novel solution containing a mixture of lump molecules, breather molecules and y-type molecules. At the same time, we analyze the dynamic behaviors of these interaction solutions and give the problems waiting to be solved.