Pulses In Optical Fibers Research Articles

WITHDRAWN: Some families of novel solutions to a third-order nonlinear Schrödinger’s equation arising in optical communication

This manuscript aims to employ an efficient integration method to extract novel optical solitons to an Schrödinger’s type equation. The considered model covers some existing variants of the equation in the literature. The technique used in this paper, which is based on a logarithmic transform, retrieves the ubiquitous types of traveling wave solutions based on elementary functions like exponential and trigonometric functions. The basic idea of this methodology is to reduce the differential equation from partial to ordinary and then apply a logarithmic transformation. To have a better intuition of the physical features of the solutions, several graphical representations have been added to the article. Further, we have studied the impact of existing parameters of the model on the acquired solutions by using software to represent them graphically. The acquired results are useful tools to figure out the features of nonlinear pulses in optical fiber. It should be noted that these techniques have not been utilized for solving in recent literature to the best of the author’s knowledge. Also, it is possible to extend the technique of the article in finding the analytical solution of similar models in nonlinear optics. All necessary calculations and drawings were done in MATHEMATICA software. • A third-order nonlinear Schrödinger equation with cubic term is studied. • We apply an effective technique based on a logarithmic transformation approach. • Several graphical representations have been proposed. • All calculations and drawings were done in MATHEMATICA software.

Dynamics of optical pulses in fiber optics with stimulated Raman scattering effect

In this paper, we discuss the propagation of optical pulses in the nonlinear optical fibers. The generalized higher-order nonlinear Schrödinger equation (NLSE) is under consideration as a governing model. The studied model is composed of group-velocity dispersion, self-phase modulation, third-order dispersion, self-steepening and stimulated Raman scattering. Researchers have been studying a wide range of natural phenomena in depth, and nonlinear science has gradually become a part of people’s consciousness. We have extracted the optical pulses in different forms like bright, dark, singular and combined solitons by assistance of recently developed integration tool, namely the new extended direct algebraic method (NEDAM). Moreover, the solutions for the hyperbolic, periodic and trigonometric functions are retrieved. Using proper parameters in numerical simulations and physical explanations, it is possible to demonstrate the importance of the findings. It is proposed that the offered method can be utilized to support nonlinear dynamical models applicable to a wide variety of physical situations. We hope that a wide spectrum of engineering model professionals will find this study to be beneficial.

Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect

In this study, the integrability conditions on mixed derivative nonlinear Schrödinger equations are the focus of this work. A. Rangwala mathematically defined these effects and dubbed this form the Rangwala–Rao equation ([Formula: see text]) in 1990. Using innovative soliton wave solutions and their interactions, we hope to better understand how dispersion affects the electric field and pulse propagation in optical fibers. Generalized Khater (GKhat.) provides unique solitary wave solutions to the [Formula: see text] problem. The pulses’ dynamical behavior through optical fibers is seen in these numerical simulations. The originality of the paper’s conclusions may be seen by contrasting our findings with those of other researchers.

New fascination of solitons and other wave solutions of a nonlinear model depicting ultra-short pulses in optical fibers

New fascination of solitons and other wave solutions of a nonlinear model depicting ultra-short pulses in optical fibers

Dynamics of optical pulses in dual-core optical fibers modelled by decoupled nonlinear Schrodinger equation via GERF and NEDA techniques

Dynamics of optical pulses in dual-core optical fibers modelled by decoupled nonlinear Schrodinger equation via GERF and NEDA techniques

Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects

We study the propagation dynamics of extremely short light pulses in an optical fiber medium exhibiting a plethora of higher-order dispersive and nonlinear effects of different nature. The wave propagation in such nonlinear media is described by an extended nonlinear Schrö dinger equation incorporating both even and odd higher-order terms. We introduce an appropriate nonlinear equation which enables us to achieve analytical shape-preserved and periodic wave solutions for the model. A new dark solitary wave is identified for the first time in the presence of all physical processes. In addition, we show that moving fronts or optical shock-type soliton solutions exist for the considered model. The periodic wave solutions are also found together with the parametric conditions for their existence. Results in this study may be useful for experimental realization of shape-preserved pulses in optical fibers and further understanding of their optical transmission properties.

Optical solitons to the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers

This paper mainly studies the optical soliton solutions of the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity describing the propagation of femtosecond pulses in optical fibers. Firstly, using traveling wave transformation, the coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity in birefringent fibers is simplified into the coupled nonlinear ordinary differential equations. Secondly, according to the trial method of polynomial of rank homogeneous equation, the optical soliton solutions of coupled cubic-quartic Sasa–Satsuma equation with Kerr law nonlinearity can be obtained. Finally, in order to explain the propagation of optical solitons, three-dimensional and two-dimensional diagrams of the obtained solutions are drawn.

On dynamical behavior for optical solitons sustained by the perturbed Chen–Lee–Liu model

This study investigates the perturbed Chen–Lee–Liu model that represents the propagation of an optical pulse in plasma and optical fiber. The generalized exponential rational function method is used for this purpose. As a result, we obtain some non-trivial solutions such as the optical singular, periodic, hyperbolic, exponential, trigonometric soliton solutions. We aim to express the pulse propagation of the generated solutions, by taking specific values for the free parameters existed in the obtained solutions. The obtained results show that the generalized exponential rational function technique is applicable, simple and effective to get the solutions of nonlinear engineering and physical problems. Moreover, the acquired solutions display rich dynamical evolutions that are important in practical applications.

Optical solitons and qualitative analysis of nonlinear Schrodinger equation in the presence of self steepening and self frequency shift

In this manuscript, the optical solitons of nonlinear Schrödinger equation (NLSE) with cubic–quintic law nonlinearity, in the presence of self-frequency shift and self-steepening, has been studied. The ultrahigh capacity propagation and transit of laser light pulses in optical fibres were described using this form of equation. To extract new results, two strong methodologies has been used. To extract the exact solution unified method has been employed. The solutions obtained by this analytical method, are in form of polynomial and rational function solution. Moreover, the validity of non-singular solutions has guaranteed by a limitation condition that is graphically illustrated in 3D. The 2D graphical representation are also used to demonstrate the influence of parameters on the predicted non-singular solutions. The other technique, used for qualitative analysis, is bifurcation. The system has been transformed into a planer dynamical system, which has been transformed into a hamiltonian system. All the possible phase portrait has been plotted by complete discrimination method. The acquired results are novel and have not been recorded before and they indicate that the proposed methodologies may be used to investigate innovative soliton solutions and phase portraits for any NLSE.

Perturbation of dispersive optical solitons with Schrödinger–Hirota equation with Kerr law and spatio-temporal dispersion

Objective:The principal purpose of this paper is to examine the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity which governs the propagation of dispersive pulses in optical fibers by proposing and using a direct algebraic form of the enhanced modified extended tanh expansion method for the first time. Our aim is not only restricted to obtaining different and more soliton solutions by proposed method for the first time in this study, but also includes examining the effect of the coefficients of self-steepening and nonlinear dispersion terms to the soliton propagation in the investigated problem. Methodology:Utilizing a traveling wave transformation, the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity can be transformed into an nonlinear ordinary differential equation (NODE). Then, the NODE is convert into a set of algebraic equations by taking account into the Riccati differential equation. Solving the set of algebraic equations, we acquire the analytical soliton solutions of the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity. In the proposed method, the modified extended tanh function method is enhanced by presenting more solutions of Riccati differential equations with the direct algebraic form, is utilized. Results:The more solutions have been established to the literature with new significant physical properties of the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity. We indicated that the presented method are effective, easily computable, and reliable in solving such nonlinear problems. Moreover, we demonstrate the dynamical behaviors and physical significance of some soliton solutions at appropriate values of parameters. Originality:A variety of soliton solutions to the perturbed Schrödinger–Hirota equation with Kerr law non-linearity by the direct algebraic form of enhanced modified extended tanh expansion method have been acquired. These solutions are dark–bright, trigonometric, hyperbolic, periodic, and singular soliton solutions. 3D, contour and 2D plots of some obtained solutions have been demonstrated to interpret the physical meaning of the equation. For some parameter values in the equation, the behavior of soliton solutions has been examined. The constraint conditions are established to confirm the existence of valid solutions. The obtained results can be effective in interpreting the physical meaning of this nonlinear system. We have seen that the proposed direct algebraic form of the enhanced modified extended tanh expansion method is a powerful mathematical technique which can be utilized to acquire the analytical solutions to different complex nonlinear mathematical models.

Derivation of optical solitons of dimensionless Fokas-Lenells equation with perturbation term using Sardar sub-equation method

This paper presents an investigation of soliton solutions for the perturbed Fokas-Lenells (pFL) equation, which has a vital role in optics, using Sardar sub-equation method. The equation models the propagation of 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 solution 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 dark, periodic, singular periodic, combined bright-dark. 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 the optic fiber industry.

Investigation of optical solitons and other solutions in optic fibers modeled by the improved perturbed nonlinear Schrödinger equation

In this manuscript, we discuss the dynamical behavior of improved perturbed nonlinear Schrödinger equation (NLSE) which propagates optical pulses in nonlinear optical fibers. The governing equation is composed of group velocity dispersion (GVD), nonlinearity, self-steeping, higher order and third order dispersion coefficients. The different kinds of solutions in the forms of bright, dark, combo and complex solitons are extracted by the assistance of recently developed integration tools, namely, the extended rational sine-cosine/sinh-cosh techniques, ϕ6-model expansion method and generalized exponential rational function method (GERFM). Moreover, the hyperbolic, Jacobi elliptic function (JEF), exponential, and trigonometric function solutions are recovered. A comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. The significance of the results is illustrated by selecting appropriate parameter values for numerical simulation and physical explanations. For the nonlinear dynamical behavior of a given system, this paper’s results can improve it and demonstrate that the applied methodology is suitable. A wide range of experts in the field of engineering models will benefit from this research, according to our opinion. The results suggest that the computational methodologies used are direct, efficient, concise, and that they may be applied to more complicated phenomena with the help of symbolic computations.

Dynamics of optical pulses in birefringent fibers without four-wave mixing effect via efficient computational techniques

In this manuscript, we discuss the dynamical behavior of Chen-Lee-Liu (CLL) equation in birefringent fibers which is modeled by two-component nonlinear Schrodinger equation (NLSE) without four-wave mixing effect. In optical fibers and other wave-guide mediums this system models the propagation of soliton flow using group velocity dispersion (GVD) and self-steeping coefficients. In the realms of maritime transport, motion, and energy, the dynamics of deep-sea waves is one of oceanography’s greatest challenges. A mathematical model of the dynamics of solitary waves in the deep ocean under a two-layer stratification yields the NLSE, and resultantly, the interaction between the two can be described by a coupled NLSE. Using two recently developed integration tools, namely the generalized exponential rational function method (GERFM) and the new extended direct algebraic method (NEDAM), the various optical pulses in the forms of bright, dark, combined, and complex solitons are extracted. Moreover, the hyperbolic, exponential, and trigonometric function solutions are recovered. In addition, a comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. By choosing appropriate parameter values for numerical simulation and physical explanations, the significance of the results is demonstrated. The results of this paper can enhance the nonlinear dynamical behavior of a given system and demonstrate the suitability of the methodology employed. This research, in our opinion, will be beneficial to a wide variety of engineering model specialists.

New single traveling wave solution in birefringent fibers or crossing sea waves on the high seas for the coupled Fokas–Lenells system

The main work of this paper is focused on construction the single traveling wave solution of the coupled Fokas–Lenells system, which is usually used to simulate the propagation of ultrashort optical pulses in birefringent fibers or crossing sea waves on the high seas. Firstly, the coupled Fokas–Lenells system is simplified into a nonlinear ordinary differential equation by traveling wave transformation and linear transformation. Then, using the well-known complete discriminant system of third-order polynomials, some single traveling wave solutions of the coupled Fokas–Lenells system are obtained including implicit solutions, rational function solutions and Jacobian function solutions.

The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning

We apply the deep learning approach to learn some nonlinear wave solutions of the Lakshmanan-Porsezian-Daniel (LPD) model characterizing the evolution of ultrashort optical pulse in optical fibers. Based on the strong universal approximation theorem, we give the initial-boundary value data and residual collocation points, choose the parameters initialization Xavier method and parameters optimization Adam and L-BFGS algorithms to construct the optimal neural network model. Then, we derive the data-driven solutions of the rogue wave, anti-dark soliton, multi-peak soliton, non-rational W-shaped soliton, rational W-shaped soliton as well as periodic-wave solutions for the LPD model. Finally, we study the parameters discovery of such model via the anti-dark soliton solution with 1% perturbation (or without perturbation).

Travelling wave solutions for hierarchy of nonlinear evolution equation description propagation pulse in optical fibers

Travelling wave solutions for hierarchy of nonlinear evolution equation description propagation pulse in optical fibers

Novel wave solutions to a generalized third-order nonlinear Schrödinger’s equation

Schrödinger’s equation and its variants play an important role in describing many well-known problems in disciplines such as mathematics and physics. Our main concern in this paper is to investigate some novel analytical solutions to a third-order generalized nonlinear Schrödinger’s equation. This equation is used to model the motion of ultra-short pulses in optical fibers. The model also includes several arbitrary parameters that introduce several well-known nonlinear models as its special case. The main achievements of the paper are determined via two efficient methodologies based upon the modified generalized exponential rational function method and a logarithmic transformation approach. In order to better examine the results, three-dimensional diagrams obtained from analytical answers have been attached to the article. These diagrams are useful tools that facilitate a better description of the capabilities of this model. One of the advantages of the method used in this research over some other techniques is that it is possible to adapt the implemented algorithm to solve other complex new problems.

Helical plasma filaments from the self-channeling of intense femtosecond laser pulses in optical fibers: publisher's note.

This publisher's note contains a correction to Opt. Lett.47, 1 (2022)10.1364/OL.445321.

Dark-soliton behaviors arising from a coupled nonlinear Schrödinger system

The principal objective of this work focuses on achieving a class of advanced and impressive N-dark–dark solitons estimations to the coupled nonlinear Schrödinger system (CNLSS) that represents the propagation of optical pluses in the model-locked fiber lasers. The achieved results will perfectly describe different nonlinear coherent structures for the behavior of the resultant solitons to this model as well as ottosecond pulses in optical fibers that play fundamental rule for all recent telecommunications. The N-dark-dark solitons arise when nonlinearities are all removed, or when there is mixture between both focusing and defocusing nonlinearities. If various focusing and defocusing solitons components are collide with each other, the energies will emerge. The N–dark-dark solitons for this model will be established by using five significant schemas that were checked before to extracting the bright, dark and other types of solitons for many nonlinear problems that arise in many branches of science. The proposed methods that are bided for this goal are the extended direct algebraic method (EDAM), the (G′G) -expansion method, the extended simple equation method (ESEM), the Paul-Painleve approach method (PPAM) and the Riccati-Bernoulli Sub-ODE method (RBSODM). The suggested methods have been checked before for many other NLPDE and continuously achieve distinct results. The achieved results will add future studies for all recent applications of the internet communications.

Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers

In this study, the Fokas system which represents the spread of irregular pulse in monomode optical fibers is investigated via the Jacobi elliptic function expansion (JEFE) method. This method is the most powerful technique to explore solutions for a wide range of various models. As a result, different solutions such as dark–bright, singular, bright, Jacobi elliptic function, and exponential solutions are obtained. In addition, 3D and 2D graphics for the obtained solutions are investigated with the assist of a computer program by assigning particular values to the parameters involved.