Novel hybrid-type solutions for the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients

In this article, the bilinear form, Backlund transformation, Lax pair and infinite conservation laws of the (3+1)-dimensional generalized Bogoyavlensky–Konopelchenko equation with time-dependent coefficients are constructed based on the Bell polynomials approach. N-soliton solutions are studied by means of introducing the complex conjugate condition technique and selecting appropriate test functions and parameters, including the hybrid solution of the a-order kink waves, b-order periodic-kink waves and c-order periodic-breather waves. The homoclinic test method is applied to investigate their dynamical interaction properties between different forms of hybrid-type solutions. Besides, a number of examples are presented by choosing different types of interactions among the hybrid-type solutions. Finally, we analyze the wave propagation direction and velocity to reflect the novel evolutionary behaviors in the three-dimensional profile of the model. These results are helpful to the study of local wave interactions in nonlinear mathematical physics.