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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]

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]

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]

The main consideration of this paper is to discuss cubic optical solitons in a polarization-preserving fiber modeled by nonlinear Schrödinger equation (NLSE). We extract the solutions in the forms of hyperbolic, trigonometric including a class of solitary wave solutions like dark, bright–dark, singular, singular periodic, multiple-optical soliton and mixed complex soliton solutions. A recently developed integration tool known as new extended direct algebraic method (NEDAM) is applied to analyze the governing model. Moreover, the studied equation is discussed with two types of nonlinearity. The constraint conditions are explicitly presented for the resulting solutions. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena. [ABSTRACT FROM AUTHOR]

The study focuses on the use of a direct algebraic approach to the analysis of the Triki–Biswas (TB) model. This model addresses the distribution of ultrashort pulses in optical fiber in the presence of non-Kerr dispersion concept and group velocity dispersion. However, using the new extended direct algebraic method, we have obtained various optical soliton solutions for the TB model. The optical soliton solutions are new and reliable compared to the existing methods. [ABSTRACT FROM AUTHOR]

In this research, a particular attention has been given on the fractional Fokas-Lenells equation via Atangana-Baleanu derivative operator that describe the propagation of short pulses in optical fibers. The integrability properties has been investigated while using the modified Khater method that we present in details. As a result, number of new soliton solutions are obtained along with constraints on some parameters that are introduced accordingly. For further details about our obtained solutions, some distinct types of solutions have been illustrated to explain more physical and dynamical behavior of the short wave pulses in the optical fibers. [ABSTRACT FROM AUTHOR]

In this paper, some new traveling wave solutions to the resonant nonlinear Schrödinger's equation (R-NLSE) with time-dependent coefficients are constructed. The well-known auxiliary equation method is applied to develop numerous interesting classes of nonlinearities, namely the Kerr law and parabolic law. Such approach provides an extensive mathematical tool to develop a family of traveling wave solutions such as bright, dark, singular and optical solutions to the nonlinear evolution model. Moreover, with the aid of symbolic computation the three-dimensional plot and contour plot have been carried out to demonstrate the dynamical behavior of the nonlinear complex model. [ABSTRACT FROM AUTHOR]

In this paper, we discuss deep visual solutions of resonant nonlinear Schrödinger's equation having full nonlinearity via taking the modified Kudryashov method. There are four types of nonlinearity in this paper. They are quadratic-cubic law, anti-cubic law, cubic-quintic-septic law and triple-power law. By performing this algorithm, logarithmical and rational solitons are deduced. [ABSTRACT FROM AUTHOR]

In this paper, we use the new defined direct algebraic method based on some particular Riccati equations to find exact solutions to a Kaup–Newell model equation. Several new solutions which represent long waves parallel to the magnetic fields have been obtained. Many solutions in generalized hyperbolic and triangular function forms, exponential or logarithmic, are expressed explicitly. Most of the solutions determined in the study are new in the related literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of cubic–quartic NLSE with the Kerr law nonlinearity via a new sub-equation method. Considered method of undetermined coefficients is applied to obtain the introduced solutions. The outcomes are useful in describing the diffusion of optical solitons. The performance of the approach is reliable, useful and gives more new general exact solutions than the other methods. [ABSTRACT FROM AUTHOR]