Abstract
The goal of this article is to investigate brand-new exact solutions to the Sawada-Kotera (SK) equation. To get at a general form solution to the SK equation, the Hirota bilinear method is used. In order to study the novel soliton solutions, several dispersion coefficients are adopted. For the first time in the literature, we analyze novel multiple-bifurcated soliton and novel rogue wave solutions of the SK equation. We study the interaction of dark soliton with rogue waves and its resonance. Another type of hybrid novel rogue wave solution is investigated, which is the fusion of bright X-shaped and rogue wave. All results are validated and displayed through graphs by using MATLAB-2020.
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