The dynamical behavior of mixed-type soliton solutions described by (2+1)-dimensional Bogoyavlensky–Konopelchenko equation with variable coefficients

Abstract

This paper investigates the (2+1)-dimensional Bogoyavlensky–Konopelchenko equation with variable coefficients via the generalized unified method. Mixed type of N-soliton solutions are obtained when and in a rational form. The propagation and the dynamical behavior of these solutions is analyzed for different choices of the arbitrary variable coefficients. When , it is verified that the velocity of the soliton cannot be influenced by the variable coefficients. Furthermore, the shape and the amplitude of the soliton cannot be affected. For , the collision between the solitons, either two kink periodic soliton solutions or two kink and anti-kink soliton solutions, are elastic whether the coefficients of the equation are constant or variable.