The nonlinear Hirota–Satsuma–Ito (HSI) equation is an important -dimensional model arising in fluid dynamics, plasmas, and other domains. In this study, the Hirota bilinear method is employed to derive a set of innovative soliton interaction solutions within the framework of the HSI system. Second-order solitons are the focus of our investigation, leading to the identification of four distinct solution types through a systematic analysis of their respective phases. These solutions are characterized by a rich spectrum of collision dynamics, encompassing phenomena, such as fusion, fission, and the intersection of trajectories. A comprehensive characterization of critical properties, including asymptotic forms, velocities, amplitudes, and interaction region lengths, is carried out. For third-order cases, seven hybrid soliton solutions are constructed, and their properties are elucidated. The results offer new analytical insights into the intricate resonant soliton behaviors permitted by the HSI system. The understanding of multidimensional soliton interactions carries significant implications spanning from optics to Bose–Einstein condensates. The Hirota bilinear technique demonstrates strong capabilities in uncovering novel soliton features in complex nonlinear wave models. Extending these methods promises additional discoveries at the intersection of nonlinear fluid dynamics, integrable systems, and soliton theory.
