Dynamic frameworks of optical soliton solutions and soliton-like formations to Schrödinger–Hirota equation with parabolic law non-linearity using a highly efficient approach

The behavior of optical soliton solutions in optical fiber theory is described by the Schrödinger–Hirota equation, a nonlinear partial differential equation with multiple applications in science and engineering. In this work, a highly effective approach for solving the Schrödinger–Hirota equation is utilized based on the modified generalized Riccati equation mapping approach. The remarkable achievement of obtaining over one hundred plus newly-formed distinct analytical soliton solutions for the governing Schrödinger–Hirota equation is accomplished through the employment of this technique. The technique employed is characterized by its power, simplicity, and adaptiveness, enabling the extraction of various forms of soliton solutions into a unified framework. As a consequence of the applications, traveling waves, bell-shaped solitons, kink waves, and combo-multisoliton wave profiles are generated. To provide valuable insights into the behavior and characteristics of the solutions, two-dimensional, three-dimensional, and corresponding contour graphs are plotted for selected solutions. These findings contribute to the improvement of theoretical knowledge regarding the Schrödinger–Hirota equation and lay the groundwork for practical implementations. The abundant soliton solutions discovered through this method have the potential to find utility in a variety of fields, including electronics, quantum physics, and optical fibers.