The N-soliton, fusion, rational and breather solutions of two extensions of the (2+1)-dimensional Bogoyavlenskii-Schieff equation

Abstract

The aim of this work is to analyze and explore the dynamics of two extensions of the Bogoyavlenskii-Schieff equation. The Hirota bilinear method is applied to the equations that arise in plasma physics. The N-soliton, fusion. rational solutions and breather solutions, as well as the interaction between M-lump and soliton solutions, are retrieved for both extended equations. The M-lump wave solutions are created from the soliton wave solutions, which are established via the Hirota bilinear method, by considering a longwave limit to the soliton wave solutions and presenting suitable conjugation conditions. The solutions for a given choice of constants are represented graphically to better understand the associated physical phenomena such as the propagation behaviors and the types of collisions.