Dynamical structures of multi-soliton solutions to the Bogoyavlenskii’s breaking soliton equations

We derive a multi-soliton solution for the Bogoyavlenskii’s breaking soliton equation by utilizing the simplified Hirota’s approach. From this multi-soliton solution, we investigate various forms of single kinky–lump-type breather solitons, double kinky–lump-type breather solitons, collision of a kink line soliton with a kinky-type breather soliton, and collision of a pair of double kinky–lump breather solitons by the appropriate selection of the involved parameters. These breathers hold unlike features in various planes even in various times. Elastic and non-elastic collisions for double kinky-type lump breather are experienced in various planes and in various times. The effect and control of the propagation direction, energies, phase shifts and shape of waves by the parameters are also analyzed. Some figures are given to illustrate the dynamics of the achieved solutions. The acquired results can enrich the dynamical properties of the higher-dimensional nonlinear scenarios in the engineering fields.