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In this paper, some analytical solutions for a model of dual-core optical fbers governed by a system of coupled non-linear Schrödinger equations (NLSEs) and the efect of the coefcient of the group velocity dispersion term on the considered model are investigated. The group velocity dispersion (GVD) has a important role in the optical wave propagation. The enhanced modifed extended tanh expansion method (eMETEM) is successfully implemented to the governing model. The NLSE system is turned into a nonlinear ordinary diferential equation (NLODE) via appropriate wave transformations. Supposing that the NLODE has solutions in the form suggested by the method and utilizing the enhanced solutions of the Riccati equation, we gain a nonlinear system of algebraic equations. The solutions of the governing model are obtained after solving the system of algebraic equations. 2D, 3D and contour illustrative fgures for the physical interpretation of the attained solutions are presented. Besides, the result of the investigation, which is related to the efect of the coefcient of the group velocity dispersion term, is presented by supporting the various graphical scheme.

In this paper, we have successfully extracted many analytic solutions for the (1+2)-dimensional Chiral non-linear Schrödinger equation (NLSE) by the enhanced modifed extended tanh expansion method (eMETEM). The considered method is a recently enhanced version of the classical modifed extended tanh expansion method. So, we have successfully extracted the abundant solutions of the (1+2)-dimensional Chiral NLSE. Using a computer algebra system program, we have verifed that all derived solutions satisfy the Chiral NLSE. The plots of some solutions are demonstrated to explain the dynamics of the solutions. It is expected that the results of the paper might be helpful for future works in traveling wave theory.

This paper presents investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, has a vital role in optics, using Sardar sub-equation method. The equation models the propagation in ultrashort light pulses in optical fibers. Using appropriate wave transformation, the pFL equation is reduced to a nonlinear ordinary differential equation (NLODE). The solutions of this NLODE equation are assumed to be in the suggested form by the Sardar sub-equation method. Hence, an algebraic equation system is obtained by substituting the trial solutions and their necessary derivatives into the NLODE. After finding the unknowns in the system, the soliton solutions of the perturbed Fokas-Lenells equation are extracted. The method produces various kinds of solitons such as the dark, singular and periodic. To show physical representations of the solitons, 2D, 3D and contour plots of the solutions are demonstrated via computer algebraic systems. It is expected that derived solutions may be useful for future works in various fields of science, especially optics and so, it may contribute to optic fiber industry.

Objective – The main objective of this paper is to investigate analytic soliton solutions of a nonlinear Schrödinger equation (NLSE), including Kudryashov’s sextic power-law nonlinearity by introducing different approaches of two efficient analytical methods. The considered equation has been recently introduced by N. A. Kudryashov to describe pulse propagation in optical fibers. The refractive index in the equation comprises six terms, each of the terms containing a power-law component. Methods – Applying a wave transformation to the considered NLSE and splitting up the real and imaginary parts, the NLSE is converted to the nonlinear ordinary differential equations (NLODEs). Then, the solutions of NLODEs are considered as suggested in the proposed method and suggested solutions that include some unknown parameters are substituted into the NLODE. An algebraic equations system is acquired by collecting the same power of the unknown function and equating all coefficients to zero. The unknown parameters in the system, and so the solutions of the NLSE, are found by solving the system. In the proposed first method, the modified extended tanh method is enhanced by proposing more solutions. The proposed second method, a different version of auxiliary methods, can remarkably reduce calculations to easily get solutions for the NLSEs with higher-order or power-law nonlinearity. Results – The two proposed methods are successfully applied to the considered NLSE and the abundant solutions of the NLSE are attained. Besides, 2D, 3D and contour graphs are demonstrated in figures for the physical illustrations of the gained solutions. Conclusion – Obtaining the solutions of NLSEs with higher-order or power-law nonlinearity has crucial importance but still challenging work. So, we propose different approaches of two efficient analytical methods, namely, enhanced modified extended tanh expansion method and an auxiliary function method. The derived results imply that the used methods are very efficient, reliable and powerful such that they can be easily implemented to many nonlinear NLSEs with higher-orders or higher power-law nonlinearities that describe real-life phenomena.

Purpose: In this paper, optical solitons of higher-order nonlinear Schrödinger equation with Kudryashov's sextic power-law of nonlinear refractive index are investigated via the direct mapping method. The considered model identifies the optical soliton pulse propagation in the optical fibers. Deriving the optical solutions of investigated model such as sextic power is critical but difficult work. The primary aim of this paper is to graphically examine the impact of power-law nonlinearity (pLawNL) and chromatic dispersion (CD) parameters clarifying self-phase modulation (SPM) in the equation on soliton behavior as well as obtaining optical soliton solutions. Methodology: To according to the used technique, we first used the complex wave transform to generate the nonlinear ordinary differential equation (NLODE) form of the nonlinear Schrödinger equation (NLSE) with Kudryashov's sextic power-law the nonlinear refractive index (SPLawNRI). Then, we were able to produce a system of linear equations in polynomial form by using the approach. Different solution sets including the values of the parameters of the studied equation and the suggested approach were produced by solving the linear system of equations. Findings: We acquired the optical soliton solutions of the main equation after inserting the sets and wave transformation into the solution functions suggested by the approach. The constraint conditions for the related solutions were suggested. We proved that the gained solutions satisfied the NLSE with Kudryashov's SPLawNRI under the suggested constraint conditions. Originality: We present contour, 3D and 2D depictions in various simulations in figures to comment the obtained solution functions. Besides, we investigate the effects of the power-law nonlinearity parameter that expresses SPM in the main equation and the parameter that are the group velocity dispersion (GVD) or chromatic dispersion (CD) on soliton behavior. The results suggest that the utilized approach is efficient, reliable, and powerful to be readily applied to various NLSEs with higher-order or higher pLawNLs that characterize real-life problems.

In this paper, we have investigated the perturbed Chen–Lee–Liu equation which describes the pulse propagation in the optical fbers, under the impact of the inter-modal dispersion, self-steepening and nonlinear dispersion terms. By using the enhanced modifed extended tanh expansion method, bright, singular, periodic singular and periodic bright solitons have been obtained and the efects of the coefcients of the inter-modal dispersion, self-steepening and nonlinear dispersion terms on the soliton’s dynamics have been examined in each case. In this respect, the review in the article has not been studied and reported before. The computations throughout this paper have been fulflled by Maple and also the graphical simulations are demonstrated via Matlab.

Purpose: When it comes to third and higher-order dispersion, the Schrödinger–Hirota equation is one of the main models developed outside the classical NLSE management models for optical soliton transmission. The cubic–quartic Fokas–Lenells equation is also one of the recently developed equations, which has importance in the field of telecommunications regarding optical soliton transmission in the absence of chromatic dispersion. In this study, in order to examine the optical solitons, the Schrödinger–Hirota equation in the presence of the chromatic dispersion and the cubic–quartic Fokas–Lenells equation discarding the chromatic dispersion were investigated. For this intent, by obtaining certain soliton types using the unified Riccati equation expansion method (UREEM), optical soliton solutions were obtained for both models and graphical representations and comments were made. Methodology: By developing appropriate computer algorithms and applying UREEM in the following ways, symbolic calculation software was made and analytical optical soliton solutions were obtained. Findings: Through computer algebra software, we plotted the obtained results via 3D, 2D views and we also illustrated the investigation of wave behavior caused by parameter change on 2D graphics. Originality: Different soliton behavior under the parameters effect of the Schrödinger–Hirota equation having chromatic dispersion and the cubic–quartic Fokas-Lenells equation is investigated and the obtained results are reported.

In this paper, we study the novel exact solutions of the ( 2 + 1 ) -dimensional Biswas–Milovic equation for the description of pulse propagation in optical fiber. We successfully constructed some important solutions, such as dark, singular, combined dark-singular soliton, singular periodic wave and rational function solutions, have been analytically obtained using the extended tanh method. These solutions might play an important role in the engineering and physics fields. It is shown that the considered method provide a straightforward and powerful mathematical tool for solving problems in nonlinear optic and other physical phenomena.