Some novel fusion and fission wave solutions in the (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko equation

The phenomena of fusion and fission are important, which have been experimentally observed in many real physical models. In this paper, by introducing a new constraint to the N-solitons, we obtain some novel fusion and fission wave solutions for the (2+1)-dimensional generalized BK equation. Numerical simulations reveal that the fusion and fission wave solutions take the shape of Y in the spatial structure. Moreover, we construct two different kinds of interaction solutions: One is the hybrid solution mixed by the fusion (fission) solitons and T-order breathers by using the constraint and complexification method. The other one is the hybrid solution consisting of the fusion (fission) solitons and L-order lumps by utilizing the constraint and long wave limit approach. Dynamical behaviors and mathematical features of these hybrid solutions are analyzed theoretically and graphically. What needs to be pointed out is that our method constitutes a generalization of what was given by Chen and Wang et al., which can be effectively used to construct the fusion and fission wave solutions of other nonlinear PDEs. Based on the wide applications of fusion and fission phenomena in nonlinear optics, fluid, biology, oceanic and atmospheric dynamics, the solutions obtained here may be helpful for experts to explain or predict some related physical phenomena.