Novel hybrid waves solutions of Sawada–Kotera like integrable model arising in fluid mechanics

Abstract

The purpose of the paper is to uncover more advanced soliton solutions for the three-component Sawada–Kotera (SK)-like equation. The Hirota bilinear (HB) method is exploited to obtain a bilinear form and general solution to the three-component SK like equation. The study explores various soliton solutions by considering multiple dispersion coefficients. The focus is on multiple bifurcated solitons, hybrid breathers, periodic lumps, and periodic rogue waves, as well as the resonance in soliton solutions. The fission or fusion processes of solitons are analyzed for specific values of parameters. From the literature, real Y-shaped and X-shaped solitons in water waves are provided. The results are presented through graphs generated using MATLAB 2021. The important feature of the proposed study is to show different behavior of the soliton in each component. The behavior of solitons, their interactions, and their transformations are all governed by the fundamental concept of energy conservation in all three cases. The amplitudes and forms of the solitons are impacted by the energy redistribution that occurs during collisions, fission, or other interactions. Understanding these energy dynamics aids in predicting how these nonlinear wave events would behave in complex systems and sheds light on the fundamental physics of these phenomena.

Keywords

• Hybrid breathers
• Bifurcation solitons
• Rogue waves
• Inelastic collision
• Fluids