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In this paper a new definition of a local fractional derivative of order α is introduced and applied to the study of the fractional nonlinear Schrödinger equation (FNLSE) with third-order dispersion and with Kerr and power laws of nonlinear refractive index. The analytical soliton solutions correspond to bright, dark and singular solitons obtained by different analytical methods. We found new optical soliton solutions with some constraints conditions that arise between the parameters of the NLSE. Typical behavior of the acquired solitons is depicted in some interesting simulations. [ABSTRACT FROM AUTHOR]

In this paper, solitons solutions of higher-order dispersive cubic–quintic Schrödinger equationincluding third-order as well as fourth-order derivatives with respect to time, that describes the dynamics of ultrashort pulses in optical fibers are investigated in detail. In this respect,a solution procedure in the locality of applied mathematics called the hyperbolic function method is appliedusing multi-linear variable separation approach (MLVSA). As an outcome, a bunch of soliton solutions isderived in conjunction with plotting dark and periodic wave solutions. The credibility of the results is examined by setting each solution back into its governing equation. Through portraits, different forms of wave solutions are depicted. Moreover, the restrictions on the parameters are also given for the existence of the obtained solutions. [ABSTRACT FROM AUTHOR]

In this paper, some optical solitons and other solutions of the Complex Ginzburg–Landau (CGL) equation with the beta time derivative are analyzed in nonlinear optics. The kink, bright, and dark solitons of the model are acquired using the (m + (G ′ ∕ G)) -expansion method. It is worth mentioning that the obtained and precise solutions are graphically displayed. To summarize, some relatively novel solutions and conclusions are obtained from the analysis of the model, which serves as a reference for the development of the Ginzburg–Landau equation in nonlinear optics. [ABSTRACT FROM AUTHOR]

The aim of this work is to find some intriguing optical soliton solutions in (2 + 1) dimensions. These soliton solutions including rational, dark, periodic, and elliptic solitons are discovered using the unified technique and the fractional order Local M-derivative to address the temporal fractional Kundu–Mukherjee–Naskar equation. It is the modification of familiar Nonlinear Schrödinger equation and used to describe the bending of an optical solitonic beam in the domain of nonlinear fiber optics and communication system. The obtained solutions are suggested with relevant conditions for their existence and displayed against 3D graphics. Also, to observe and identify the effect of fractional-order parameter on constructed solutions is shown through 2D graphs. The findings highlight that the suggested approach is simple, efficient and successful in determining the exact solution of models in optics, engineering, and other nonlinear sciences. [ABSTRACT FROM AUTHOR]