On the Complexiton Solutions to the Conformable Fractional Hirota–Satsuma–Ito Equation

This study analyzes the Hirota–Satsuma–Ito equation, which discusses the propagation of unidirectional shallow-water waves and the interactions between two long waves with different dispersion forms. For the proposed equation, the sine-Gordon expansion method has been considered. This method is derived from the sine-Gordon equation. Different types of solutions, namely, bright, periodic, and dark-bright soliton solutions, are derived. When these solutions are compared to other previously published research, to our knowledge, the study concludes that they are innovative, and this method was not applied to this equation. The validation of the obtained solutions is verified and plotted as three-dimensional figures to comprehend physical phenomena. With the proper parameter values, distinct graphs are created to convey the physical representation of specific solutions. The results of this paper show that the method effectively improves a system’s nonlinear dynamical behavior. This study will be useful to a wide range of engineers who specialize in engineering models. The findings show that the computational approach is successful, simple, and even applicable to complex systems.