Variety interaction between k-lump and k-kink solutions for the generalized Burgers equation with variable coefficients by bilinear analysis

Abstract

In this paper, we study the generalized Burgers equation with variable coefficients which is considered in soliton theory and generated by considering the Hirota bilinear operators. We retrieve some novel exact analytical solutions, including 2-lump-type wave solutions, interaction between 2-lump and one kink wave solutions, interaction between two lump and two kink wave solutions, interaction between two lump and two kink wave solutions of another type, interaction between two lump and one periodic wave solutions, interaction between two lump and kink-periodic wave solutions, and interaction between two lump and periodic-periodic wave solutions for the generalized Burgers equation by Maple symbolic computations. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Through the way of resetting different space constants, we adjust the coordinates of kink-type waves in order for them colliding with the breather wave, after that, the transformed kink-type waves gradually swallow the breather wave. Lastly, the graphical simulations of the exact solutions are depicted.