An expansion method for generating travelling wave solutions for the (2 + 1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients

This paper presents a new approach to studying nonlinear evolution equations with variable coefficients and applies it to the Bogoyavlensky-Konopelchenko equation. The Bogoyavlensky-Konopelchenko equation, which describes the interaction between a long wave and a Riemann wave in a special fluid, has many applications in fluid dynamics of mathematical physics. Most studies in the literature focus on the Bogoyavlensky-Konopelchenko equation with constant coefficients. This can lead to deficiencies in the understanding of the physical phenomena revealed by the model. To overcome this limitation, terms with time-varying coefficients are introduced into the Bogoyavlensky-Konopelchenko equation. With the addition of these terms, the model is brought closer to the real problem and the physical phenomenon can discussed with more freedom. This study has three main focal points. Firstly, it introduces a novel approach designed for nonlinear evolution equations characterized by variable coefficients. Secondly, the proposed method is applied to generate solutions for the Bogoyavlensky-Konopelchenko equation, showcasing distinctions from existing literature. Finally, the effects of time-varying coefficients on solitons and their interactions with each other in the generated travelling wave solutions are analysed in detail under certain restrictive conditions. The results shed light on the physical behavior of the Bogoyavlensky-Konopelchenko equation with variable coefficients and contribute to a better understanding of similar models. The proposed method opens new possibilities for the study of nonlinear evolution equations with variable coefficients and provides avenues for analytical investigation of their solutions.