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The generalized Riccati equation (GRE) together with the basic simplest equation method (SEM) is investigated to deal with the nonlinear fractional differential equations. This method contains the auxiliary equation φ ′(η) = Δ φ (η)2 + λφ (η) + Ω with arbitrary non-variable coefficients that gives a variety of soliton solutions. Here, we apply this technique to obtain novel optical solitons solutions for the perturbed Gerdjikov–Ivanov (PGI) equation with truncated M-fractional derivative. 3D and contour plot diagrams are drawn to illustrate the efficacy of the conformable fractional order on the behavior of some of those solutions. The secured solutions of this model have dynamic and significant justifications for some real-world physical occurrences. [ABSTRACT FROM AUTHOR]

A variety of soliton solutions of a common shape of the nonlinear Schrödinger equation with time-dependent coefficients is investigated via the extended tanh expansion method. This model was appealing to many researchers when its coefficients vary with time because they are closer to the naturalistic circumstances and they have a variety of soliton structures than the other classical ones (they able to model the slowly-changing inhomogeneities, external forces and non-uniformities of boundaries). A bundle of strands can be utilized to create a gadget called an endoscope or a fiberscope. Typically a long, lean test that can be put into a little gap, that will send a picture of what is interior through the fiber of a camera. Endoscopes are used by doctors to see inside the human body and are sometimes used by engineers to see inside tight spaces in machines. The four kinds of bizarre non-Kerr laws deliberated in this work are a quadratic-cubic law, an anticipates law, a cubic-quintic-septic law, and the triple-power law. Finally, 3D graphs are drawn for some acquired solutions. These solutions show that the suggested scheme is effective, reliable and simple for solving different types of nonlinear differential equations. [ABSTRACT FROM AUTHOR]

This article presents a technique for finding solitary wave solutions of higher-order nonlinear differential equations. Time fractional nonlinear differential equations that have hierarchy contain higher orders are presented for the description of highly dispersive optical solutions. We find optical solitons with high dispersion order for time-fractional nonlinear perturbed Schrödinger equations of the fourth and sixth orders. Some figures are investigated to show the accuracy of the solutions obtained. [ABSTRACT FROM AUTHOR]

The present paper explores the generalized third-order nonlinear Schrödinger (GTONLS) equation which is used to model ultra-short pulses in optical fibers. The analysis is carried out systematically by adopting a complex transformation for reducing the GTONLS equation to a couple of nonlinear ordinary differential equations (NLODEs) with specific conditions such that the resulting NLODEs can be solved through the use of well-designed techniques such as the exp a -function and unified methods. As an outcome, different wave structures including dark and bright solitons as well as Jacobi elliptic solutions to the model are formally constructed. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic nonlinear Schrödinger equation (NLSE) forced by multiplicative noise that represents the temporal change of fluctuations is examined in a more extended form. Symmetry reduction (nonclassical symmetry) is used to convert the nonlinear partial differential equation into a nonlinear ordinary differential equation to obtain new optical soliton solutions. The Sardar sub-equation method is suggested to solve this stochastic nonlinear problem. The obtained stochastic solitons illustrate the dispersion of waves in optical fiber transmissions. This approach enables us to study a wide range of solutions with significant physical perspectives, including dark solitons, bright solitons, singular and periodic solitons with their noise term effects involved in Brownian motion based on the Itô sense. The noise term effects on the solitons are presented using 3D and 2D graphs. The results and calculations show the significance, accuracy and efficiency of the method. Various stable and unstable nonlinear stochastic differential equations that are found in mathematics, physics and other applied areas can be solved using this technique. • New stochastic solitons solutions for the stochastic nonlinear Schrödinger equation were constructed. • The solutions of this model were found using the Sardar sub-equation method. • The Physical meaning for the obtained solutions is graphically investigated. [ABSTRACT FROM AUTHOR]