Dromion solutions of nonlinear BKK equations using the improved F-expansion method

Abstract

This article investigates a (2 + 1)-dimensional nonlinear Broer–Kaup–Kupershmidt (BKK) equation and proposes an improved F-expansion method for obtaining analytical soliton solutions. We introduce the F-expansion technique, which involves a Riccati equation and hyperbolic functions. Using this approach, various solutions are obtained and some structures are constructed and classified into three categories: dromion solutions, local excitations and self-similar fractal structures. These solutions contribute to understanding the (2 + 1)-dimensional BKK and give vital insights into wave distributions. To obtain the dynamics of the solutions, some results are discussed and some local excitations and self-similar fractal structures (FSs) are presented. For the trial functions are emerged into the dromion solutions, the fractal structures which are self-similar are observed. The physical insight and the dynamics of the dromion solutions describing the wave propagation transmission in optical physics are discussed for different selections of rational polynomial trial functions in the solutions. The significance of this work lies in the successful application of the proposed method to achieve soliton solutions of (2 + 1)-dimensional BKK. Through symbolic calculation, the analytic soliton solutions are extracted, which is beyond the efforts of the previous literature. This method provides a new perspective for studying the BKK equation and its solutions. The results obtained enhance our understanding of the BKK behaviour and pave the way for the next work in this area.