Similarity reduction and multiple novel travelling and solitary wave solutions for the two-dimensional Bogoyavlensky–Konopelchenko equation with variable coefficients

In this study, the two-dimensional Bogoyavlensky–Konopelchenko equation with variable coefficients (vcBK) which describes the interaction of Riemann waves has been solved two times by using the balance technique. First, the balance procedure was used to reduce the vcBK equation into a fourth-order nonlinear ordinary differential equation and by its implementation again composed with the auxiliary method, many novel periodic, kink and solitary wave solutions were obtained for the vcBK equation. Second, the balance method was used to construct the Bäcklund transformation for the vcBK equation, by which n-soliton solutions were obtained. Finally, some figures were given to show the soliton interaction for different values of the variable coefficients.