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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. [ABSTRACT FROM AUTHOR]

In this paper, we use two efficient mathematical approaches to obtain a variety of soliton solutions to the (3+1)-dimensional Schrödinger equation: the generalized Riccati equation mapping method and the newly proposed modified generalized exponential rational function method. These techniques extracted standard, illustrative, rich dynamical structures, and further comprehensive soliton solutions and traveling wave solutions involving hyperbolic form, trigonometric form, and exponential form. The obtained results have been verified by placing them back into the mentioned nonlinear partial differential equation via symbolic computation in Mathematica. Thereafter, the graphical demonstrations of some attained solutions are discussed for a better understanding of the physical phenomenon. We have portrayed the three-dimensional, contour plot, and two-dimensional graphs for different parametric values. The attained results demonstrate the generalized Riccati equation mapping method and modified generalized exponential rational function techniques for extracting soliton solutions to nonlinear partial differential equations are efficient, compatible, and reliable in nonlinear sciences, optical fibers, and engineering. [ABSTRACT FROM AUTHOR]