Multi-soliton solutions of the Sawada-Kotera equation using the Hirota direct method: Novel insights into nonlinear evolution equations

Recently, mathematicians, engineers, and scientists have explored the unique characteristics and potential applications of multi-solitons, which is an expanding domain of study. There are various approaches to obtaining multi-soliton solutions of an integrable system, such as the Bäcklund transform, the nonlinear transform method, the Hirota direct method, etc. But each approach has some own characteristics and attributes; however, the Hirota direct method is dominant among them and provides further multi-soliton solutions of nonlinear evolution equations. In this article, we use the Hirota direct method to investigate the single-soliton, double-soliton, and triple-soliton solutions, known as multi-soliton solutions, of the integral Sawada-Kotera equation. We also demonstrate and discuss the effects of amplitude on the fluctuation of wave number in different ranges by comparing 2-D and 3-D plots.