Stability analysis and optical soliton solutions to the nonlinear Schrödinger model with efficient computational techniques

In this research work, we elucidate the dynamical behavior of optical solitons to the generalized (1 + 1)-dimensional unstable space–time fractional nonlinear Schrödinger (gf-UNLS) model emerging in nonlinear optics. A variety of nonlinear dynamical optical soliton structures are extracted in different shapes like hyperbolic, trigonometric, and plan wave solutions including some specifically known solitary wave solutions like bright, dark, singular, and combo solitons by engaging three efficient mathematical tools namely the extended sinh-Gordon equation expansion metho, (G′G2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{G^{\prime }}{G^2}$$\end{document})-expansion function method and the modified direct algebraic method). Besides, we also secure singular periodic wave solutions with unknown parameters. All the reported solutions are verified by putting back to the original equation through soft computation Mathematica. The modulation instability analysis for the given nonlinear Schrödinger model is also observed. The outcomes reveal that the governing model theoretically possesses immensely rich structures of optical soliton solutions. The physical characterization of some obtained results are figured out graphically in 3D, and their corresponding contour profiles by using different scales of parameters to clarify and visualize the physical features of the problem.