Dynamical behavior of multiwave interaction solutions for the (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation

The (3+1)-dimensional Kadomtsev-Petviashvili-Bogoyavlensky-Konopelchenko equation is used to simulate the evolution of shallow water waves with weakly nonlinear restorative forces and waves in a strong magnetic medium, as well as ion acoustic waves and stratified ocean internal waves in incompressible fluids. The bilinear representation, Backlund transformation, Lax pair and infinite conservation laws of the equation are systematically constructed by using the Bell polynomial method. Based on the Hirota bilinear method and some propositions, several new analytic solutions are studied, including the hybrid solutions among the lump waves and periodic waves, mixed solutions between the lump waves and periodic waves, mixed solutions between periodic waves. The dynamic behaviors of these analytical solutions are studied by means of three-dimensional diagrams, and some new structures and properties of waves are found. The research results provide a new method for us to explore the model. The obtained results can be widely used to report various interesting physical phenomena in the field of shallow water waves, fluid mechanics, ocean dynamics and other similar fields.