Fission and fusion solutions of the (2+1)-dimensional generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation: case of fluid mechanics and plasma physics

In this work, the (2+1)-dimensional gKDKK equation is the research object. On the basis of Hirota bilinear, a new constraint condition is added to obtain the fission and fusion solutions. They are also called y-type solutions because of their shape like the letter Y. When N= 2 , N= 3 and N= 4 , the y-type solutions of the (2+1)-dimensional gKDKK equation are studied, numerical simulations are carried out, and the corresponding density diagrams are drawn. In combination with velocity resonance method, mode resonance method and long-wave limit method, a variety of molecules mixing interaction are obtained, including y-type molecules, resonant soliton molecules, breather molecules, lump molecules, and their density diagrams are simulated. The motivations of this paper are to obtain the fission and fusion solutions of the (2+1)-dimensional gKDKK equation, and to study their interaction with a variety of molecules. The fission and fusion solutions of the (2+1)-dimensional gKDKK equation are obtained, and their time-varying images are drawn. During the y-type molecules’ interaction with other molecules, their shape do not change, which means there is no increase or loss of energy.