Abundant fission and fusion solutions in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation. By introducing some new constraint conditions to its N-solitons, the fission and fusion are obtained. Numerical figures show that the two types of solutions look like the capital letter Y in spatial structures. Then, by taking a long wave limit approach and complex conjugation restrictions, some hybrid resonance solutions are generated, such as the interaction solutions between the L-order lumps and Q-fission (fusion) solitons, as well as hybrid solutions mixed by the T-order breathers and Q-fission (fusion) solitons. Dynamical behaviors of these solutions are analyzed theoretically and numerically. The results obtained can be helpful for understanding the fusion and fission phenomena in many physical models, such as the organic membrane, macromolecule material and even-clump DNA, plasmas physics, and so on.