Diverse optical solitons to nonlinear perturbed Schrödinger equation with quadratic-cubic nonlinearity via two efficient approaches

Abstract

In this study, the nonlinear perturbed Schrödinger equation(NPSE) with nonlinear terms as quadratic-cubic law nonlinearity media with the beta derivative is investigated and this investigated model is considered an icon in the field of optical fibers where it describes the wave function or state function of the optical system. Numerous solutions are extracted by engaging two novel schemes known as generalized -expansion method (GEEM) and rational extended sinh-Gordon equation expansion method (REShGEEM) in distinct forms such as bright, dark, singular and combinations of these solutions. In addition, plane wave, periodic and exponential solutions are also recovered. Using the computer application Wolfram Mathematica 11, the dynamic structure and physical characterization of some observed solutions are vividly depicted by sketching different plots. Comparing our new results with well-known literature is also given which justifies the novelty of this work. Obtained results will hold a significant place in the field of nonlinear optical fibers and suggest that the proposed methods are very influential and effective tools for solving more complex nonlinear partial differential equations in mathematical physics, engineering and nonlinear optics.