Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion

The main concentration of this article is to extract pure-cubic optical solitons in nonlinear optical fiber modeled by nonlinear Schrödinger equation (NLSE). The governing model is discussed the with the effect of third-order dispersion, Kerr law of nonlinearity and without chromatic dispersion. We extract the solutions in different forms like, Jacobi’s elliptic, hyperbolic, periodic, exponential function solutions including a class of solitary wave solutions such that bright, dark, singular, kink-shape, multiple-optical soliton, and mixed complex soliton solutions. Recently developed integration tools known as [Formula: see text] -model expansion method, generalized exponential rational function method (GERFM) and generalized Kudryashov method are applied to analyze the governing model. The studied model is also discussed by the concept of modulation instability (MI) analysis. The constraints conditions are explicitly presented for the resulting solutions and singular periodic wave solutions are recovered. Furthermore, for explaining the solutions in physical phenomena, the three dimensional, two dimensional, and their related contours graphs are plotted under the selection of appropriate parameters. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena. The results show that the studied equation theoretically has extremely rich pure-cubic optical structures of nonlinear fiber relevance.