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This paper addresses Radhakrishnan--Kundu--Lakshmanan equation that arises in the study of soliton dynamics in optical fibers. The bifurcation analysis is carried out and the phase portraits are displayed. The complete discriminant analysis also leads to solitons and other solutions to the model. [ABSTRACT FROM AUTHOR]

This paper recovers quiescent optical solitons that are self-sustaining, localized wave packets that maintain their shape and amplitude over long distances due to a balance between nonlinearity and dispersion. When a soliton is in a state of quiescence, it means that it is stationary in both space and time. Quiescent optical solitons are typically observed in optical fibers, where nonlinearity and dispersion can lead to the formation of solitons. The concatenation model is considered to understand the behavior of optical pulses propagating through nonlinear media. Here, we consider the familiar nonlinear Schrödinger equation, the Lakshmanan–Porsezian–Daniel equation, and the Sasa–Satsuma equation. The current paper also addresses the model with nonlinear chromatic dispersion, a phenomenon that occurs in optical fibers and other dispersive media, where the chromatic dispersion of the material is modified by nonlinear effects. In the presence of nonlinearities, such as self-phase modulation and cross-phase modulation, the chromatic dispersion coefficient becomes a function of the optical intensity, resulting in nonlinear chromatic dispersion. A full spectrum of stationary optical solitons, along with straddled stationary solitons, are obtained. There are four integration schemes that made this retrieval possible. The numerical simulations are also included for these solitons. The parameter constraints also indicate the existence criteria for these quiescent solitons. [ABSTRACT FROM AUTHOR]

In the present investigation, we employed the Jacobi elliptic function (JEF) method to invoke the perturbed nonlinear Schrodinger equation with self-steepening (SS), self-phase modulation (SPM), and group velocity dispersion (GVD), which govern ¨ the propagation of solitonic pulses in optical fibres. The proposed algorithm proves the existence of the family of solitons in optical fibers. Consequently, chirped and chirp free W-shaped bright, dark soliton solutions are obtained from dn(ξ ), cn(ξ ) and sn(ξ ) functions. The final results are displayed in three-dimensional plots with specific physical values of GVD, SPM and SS for an optical fiber. [ABSTRACT FROM AUTHOR]

Purpose: In this article, two main subjects are discussed. First, the nonlinear Schrödinger equation (NLSE) with an anti-cubic (AC) nonlinearity equation is examined, which has a great working area, importance and popularity among the study areas of soliton behavior in optical fibers, by using the enhanced modified extended tanh expansion method and a wide range of optical soliton solutions is obtained. Second, the effects of AC parameters on soliton behavior are examined for each obtained soliton type. Methodology: In order to apply the method, the non-linear ordinary differential equation form (NLODE) of the investigated NLSE-AC is obtained by applying the defined wave transformation. Then, with the help of the proposed algorithm for the NLODE form, polynomial form, an algebraic equation system is obtained by setting the coefficients of this form to zero, and the solution of this system is also obtained. After determining the suitable solution set, the optical soliton solution of the investigated problem is obtained with the help of the serial form of the proposed method, a Riccati solution and wave transform. After checking that the solution satisfies the investigated problem, 3D and 2D graphics are obtained for the special parameter values and the necessary comments are made in the relevant sections. Findings: With the proposed method, many optical soliton solutions, such as topological, anti-peaked, combined peaked-bright, combined anti-peaked dark, singular, combined singular-anti peaked, periodic singular, composite kink anti-peaked, kink, periodic and periodic, with different amplitudes are obtained, and 3D and 2D representations have been made. Then, the effect of AC parameters on the soliton behavior in each case has been successfully studied. It has been shown that AC parameters have a significant effect on the soliton behavior, and this effect changes depending on the soliton shape and the parameters. Moreover, providing and maintaining the delicate balance between the soliton shape and the parameters and the interaction of the parameters with each other involves great difficulties. Originality: Although some soliton types of the NLSE-AC equation have been presented for the first time in this study, there is no study in the literature showing the effect of AC parameters on soliton behavior, especially for the NLSE-AC equation. [ABSTRACT FROM AUTHOR]

This work recovers cubic-quartic optical solitons with dispersive reflectivity in fiber Bragg gratings and parabolic law of nonlinearity. The Lie symmetry analysis first reduces the governing partial differential equations to the corresponding ordinary differential equations which are subsequently integrated. This integration is conducted using two approaches which are the modified Kudryashov's approach as well as the generalized Arnous' scheme. These collectively yielded a full spectrum of cubic-quartic optical solitons that have been proposed to control the depletion of the much-needed chromatic dispersion. They range from bright, dark, singular to combo solitons. These solitons are considered with dispersive reflectivity, which maintains the necessary balance between chromatic dispersion and nonlinear refractive index structure for an uninterrupted transmission of solitons along intercontinental distances. Their respective surface and contour plots are also exhibited. A few closing words are included with some prospective future avenues of research to extend this topic further. [ABSTRACT FROM AUTHOR]

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist. [ABSTRACT FROM AUTHOR]

This paper obtains highly dispersive optical solitons in fiber Bragg gratings with the Kerr law of a nonlinear refractive index. The generalized Kudryashov's approach as well as its newer version makes this retrieval possible. A full spectrum of solitons is thus recovered. [ABSTRACT FROM AUTHOR]

This paper recovers cubic-quartic perturbed solitons in fiber Bragg gratings with quadratic-cubic law nonlinear refractive index. The unified Riccati equation expansion method and the modified Kudryashov’s approach make this retrieval of soliton solutions possible. The parameter constraints, for the existence of such solitons, are also presented. [ABSTRACT FROM AUTHOR]

The parameter dynamics of solitons, propagating through optical fibers, is emerged from the usage of variational principle. The anti-cubic nonlinearity and its generalized version are studied. This study reveals that the center position does not affect the dynamics of different parameters and only soliton power and linear momentum are conserved quantities. [ABSTRACT FROM AUTHOR]

Optical solitons with fiber Bragg gratings and polynomial law of nonlinear refractive index are addressed in the paper. The auxiliary equation approach together with an addendum to Kudryashov's method identify soliton solutions to the model. Singular periodic solutions emerge from these integration schemes as a byproduct. [ABSTRACT FROM AUTHOR]

This paper reveals bright, dark and singular solitons in fiber Bragg gratings with dispersive reflectivity having parabolic form of nonlinearity. The method of undetermined coefficients yielded such soliton solutions. The existence criteria of such solitons are also enumerated that are listed as constraint conditions. [ABSTRACT FROM AUTHOR]

This paper studies optical solitons in fiber Bragg gratings, that appear with quadratic–cubic nonlinearity, in presence of dispersive reflectivity. The extended trial function scheme revealed bright and singular optical soliton solutions to the model. The phase-matching condition was adopted to this model. [ABSTRACT FROM AUTHOR]

This paper retrieves bright, dark and singular solitons of both types for Bragg gratings with dispersive reflectivity. The method of undetermined coefficients is the integration algorithm adopted in this paper. Several constraints guarantee the existence of such solitons. [ABSTRACT FROM AUTHOR]

This paper applies extended trial function scheme to retrieve bright and singular optical soliton solutions to fiber Bragg gratings that maintains parabolic law nonlinearity. The existence criteria for the solitons are presented. Additional solutions, such as rational waves and periodic solutions, naturally emerge from the scheme as a byproduct. [ABSTRACT FROM AUTHOR]

Abstract This paper obtains conservation laws of Chen–Lee–Liu equation in optical fibers. The conserved densities are retrieved by Lie symmetry analysis and the conserved quantities are finally presented from bright 1-soliton solutions that are reported in the past. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a new model for soliton transmission through optical fibers where self-phase modulation is negligibly small and hence removed. The model however includes spatio-temporal dispersions, of second and third order, to compensate for low group velocity dispersion. The balance for sustaining solitons is provided by nonlinear dispersion terms that are considered in this model. [ABSTRACT FROM AUTHOR]

We introduce a novel class of derivative nonlinear Schrödinger equations incorporating a pure derivative nonlinearity term of arbitrary order. This new model can be used as a basis for the description of femtosecond pulse propagation in highly nonlinear optical fibers beyond the Kerr limit. We demonstrate that this nonlinear wave equation offers a very rich model that supports envelope soliton solutions of different waveforms and shapes. A new form of phase structure that shows nontrivial chirping which is a nonlinear function of the wave intensity, characterizes these solutions. The reported solutions are necessarily of the soliton-type containing rational, regular (hyperbolic-secant) and soliton-like solutions of the bright-type as well as kink-type envelopes. The formation conditions for the existence of these structures are also reported. [ABSTRACT FROM AUTHOR]

Dark and bright with singular solitons shall be yielded to Fokas–Lenells equation which describes soliton dynamics in optical fibers. The two integration schemes that are applied in this context are the modified simple equation method and the trial equation method. Additional solutions, besides, optical solitons, are recovered. [ABSTRACT FROM AUTHOR]

This paper retrieves bright and singular dispersive optical soliton solutions in optical fibers. The governing model is Schrödinger–Hirota equation. The existence criteria for these solitons are also enumerated. [ABSTRACT FROM AUTHOR]

The trial equation method is applied to obtain soliton solutions to Lakshmanan–Porsezian–Daniel model in optical fibers, PCF and metamaterials. This integration procedure is implemented into the model with three forms of nonlinearity. Bright, dark and singular soliton solutions are recovered with conditions that guarantee their existence. [ABSTRACT FROM AUTHOR]

This paper examines soliton dynamics of sub pico-second pulses modeled by Kaup–Newell equation. The modified simple equation scheme and trial equation approach retrieves dark, bright as well as singular solitons to the model. The constraint relations guarantee the existence of such solitons. [ABSTRACT FROM AUTHOR]

Optical solitons in birefringent fibers with the effect of four-wave mixing having both parabolic and Kerr law nonlinearity are obtained by the modified simple equation scheme and the trial equation approach. Dark, bright as well as singular soliton type solutions are derived. Also, the two integration schemes give rise to additional solutions such as singular periodic solutions. [ABSTRACT FROM AUTHOR]

The soliton dynamics in optical fibers with Fokas–Lenells equation is illustrated in this paper. Bright, dark and singular soliton solutions are retrieved along with few forms of combo-soliton solutions that also naturally emerged from the three integration schemes applied to the model. The existence criteria of these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies differential group delay in optical fibers with coupled Fokas–Lenells equation. Two integration schemes are adopted. They are trial equation method and modified simple equation scheme. Bright, dark and singular soliton solutions are retrieved together with their respective existence criteria that are also presented. [ABSTRACT FROM AUTHOR]

The extended trial function approach was successfully applied to determine soliton solutions to Fokas–Lenells equation. Bright, dark and singular soliton solutions are retrieved with the aid of this algorithm. In addition, several other solutions also emerged from this scheme whose limiting case led to optical solitons. [ABSTRACT FROM AUTHOR]

This paper retrieves optical soliton solutions with fractional temporal evolution by the aid of generalized Kudryashov's method. There are four types of nonlinear fibers that are studied here. Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper secures chirped bright and singular soliton solutions in an optical metamaterial that is considered with parabolic law nonlinearity and self-steepening effect. The extended trial function method is the integration scheme adopted in this paper. Several other solutions such as singular periodic waves and elliptic functions naturally emerge as a byproduct of this scheme. [ABSTRACT FROM AUTHOR]

This paper retrieves optical Gaussons in DWDM network by the aid of extended trial function approach. The model is considered with inter-modal dispersion and log-law nonlinearity. The constraint conditions assure the existence of such pulses across the network. [ABSTRACT FROM AUTHOR]

The Lie symmetry analysis is applied to Lakshmanan–Porsezian–Daniel model, with Kerr and power law nonlinearity, to retrieve optical soloiton solutions. Singular soliton solutions are available by the application of this algorithm. [ABSTRACT FROM AUTHOR]

This paper employs the extended trial equation method to retrieve chirped optical soliton solutions to Chen–Lee–Liu model that describes pulse propagation through optical fibers. Bright and singular optical soliton solutions are recovered by the application of this algorithm. As a byproduct, singular periodic solutions fall out. These soliton solutions are obtained with constraint conditions that are also presented. [ABSTRACT FROM AUTHOR]

This paper addresses the dynamics of optical solitons in the presence of perturbation terms by the aid of three integration schemes. They are modified simple equation method, trial equation scheme, and the extended trial equation scheme. There are three types of nonlinearities that are studied in this paper which are Kerr law, power law, and logarithmic law. The constraint conditions for the existence of these solitons are also presented. [ABSTRACT FROM AUTHOR]

Investigated in this work is the nonlinear Schrödinger equation with space-dependent parameters, which models the propagation of optical solitons in spatially inhomogeneous optical fiber with detuning, spatiotemporal dispersion, intermodal dispersion, and fiber gain or loss. Through the ansatz scheme, analytical bell, kink, and singular soliton solutions under certain coefficient constraints are obtained. [ABSTRACT FROM PUBLISHER]

This paper revisits highly dispersive optical solitons in birefringent fibers, with Kerr law nonlinearity, from a numerical perspective. The Laplace–Adomian decomposition scheme reveals the spectral display of bright and dark optical solitons that are with differential group delay. The error measure is also displayed that is stunningly low. [ABSTRACT FROM AUTHOR]

In this paper, the resonant nonlinear Schrödinger’s equation is studied with four forms of nonlinearity. This equation is also considered with time-dependent coefficients. The simplest equation method is applied to solve the governing equations and then exact 1-soliton solutions are obtained. It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics. [ABSTRACT FROM PUBLISHER]

This paper reports the first analytical demonstration of propagation of algebraic solitary waves accompanied with a nonlinear chirp in optical fibers governed by the Kundu–Eckhaus equation. Both chirped dark and bright algebraic solitary waves can exist in the system with higher-order effects such as Raman effect and quintic nonlinearity. The chirp associated with each of these algebraic solitary waves is shown to be dependent on the intensity of the wave. It is found that the Raman process has a profound impact in the chirp of these localized pulses. • The propagation of ultrashort light pulses in optical fibers is studied. • The model equation incorporates the quintic nonlinearity and Raman effect is considered. • Both chirped dark and bright algebraic solitary waves are reported. [ABSTRACT FROM AUTHOR]

This paper studies the perturbation of the improved version of the nonlinear Schrödinger's equation that governs the propagation of solitons through nonlinear optical fibers. The semi-inverse variational principle is employed in order to obtain an analytical soliton solution in presence of the perturbation terms. There are three types of nonlinearity that will be studied. They are Kerr law, power law and the log law. The constraint conditions will naturally fall out in order for the soliton solutions to exist. The numerical simulations supplement the analytical results for each of the three laws of nonlinearity. [ABSTRACT FROM AUTHOR]

Abstract: The Schrödinger–Hirota equation governs the propagation of optical solitons in a dispersive optical fiber. In this paper, this equation will be solved by the ansatz method for bright and dark 1-soliton solution. The power law nonlinearity will be assumed. By using the tanh method, some additional solutions will be derived. Finally, the numerical simulations will be given. [Copyright &y& Elsevier]

In this paper an analytical expression for an optical soliton is obtained with the aid of He's semi-inverse variational principle in the presence of third- and fourth-order dispersion as well as inter-modal dispersion. Three laws of nonlinear media are considered in this paper: the Kerr law, the power law and the log law. [ABSTRACT FROM PUBLISHER]

This paper studies optical solitons with linear attenuation and bandpass filters. The Kerr and power laws of nonlinearity are considered. The governing equations are integrated by the aid of He's semi-inverse variational principle. The parameter domains are identified. [ABSTRACT FROM AUTHOR]

This paper obtains the parameter dynamics of super-sech optical solitons propagating through optical fibers. The variational principle is applied to obtain these parameter dynamics. Both polarization preserving fibers as well as birefringent fibers are studied in this paper. The study is then finally extended to the case of DWDM systems. The adiabatic parameter dynamics of soliton parameters is then obtained in the presence of perturbation terms. The numerical simulations are also obtained to complete the analysis. [ABSTRACT FROM AUTHOR]

This paper studies the propagation of solitons through optical fibers with dispersion management. The adiabatic variation of the soliton parameters, due to the presence of perturbation terms, is obtained. The dynamics is studied for the case of polarization-preserving fibers, while the types of pulses that are considered here are Gaussian, super-Gaussian and supersech. The perturbation terms that are taken into consideration are both local and nonlocal. [ABSTRACT FROM AUTHOR]

The transmission speed of optical network strongly depends on the impact of higher order dispersion. In presence of coherent crosstalk, which cannot be otherwise controlled by optical filtering, the impact of higher order dispersions becomes more pronounced. In this paper, the general expressions, that describe pulse deformation due to second- and fourth-order dispersions in a single-mode fiber, are given. The responses for such even-order dispersions, in presence of coherent crosstalk, are characterized by waveforms with long trailing edges. The transmission quality of optical pulses, due to both individual and combined influence of second- and fourth-order dispersions, is studied in this paper. Finally, the pulse shape and eye diagrams are obtained. [ABSTRACT FROM AUTHOR]

Abstract: The higher-order multiple-scale asymptotic analysis is carried out for the Gabitov–Turitsyn equation that governs the propagation of dispersion-managed solitons through optical fibers. The averaged equation, with the consideration of higher-order terms, provides an in-depth understanding of the soliton propagation through an optical fiber. The polarization preserving fibers as well as birefringent fibers are considered in this paper. Finally, the study is extended to the case of multiple channels, namely dispersion-flattened fibers. [Copyright &y& Elsevier]

The evolution of quasi-linear pulses in optical fibers, with strong dispersion management, is studied analytically. The nonlinear terms of the Gabitov–Turitsyn equations are analyzed asymptotically. In this paper, the polarization preserving fibers as well as the birefringent fibers are studied. Finally, the study is extended to the case of multiple channels, namely dispersion flattened fibers. The numerical simulations support the analysis. [Copyright &y& Elsevier]

The dynamics of optical solitons with dispersion-management propagating through optical fibers with damping and amplification is studied. A multiple-scale perturbation expansion method is used to analyze the nonlinear Schrödinger's equation that governs the propagation of such solitons. In this paper we have considered both polarization preserving as well as birefringent fibers. Finally, the case of dense wavelength-division-multiplexed soliton system is also considered. [ABSTRACT FROM AUTHOR]

The propagation of solitons through optical couplers is studied here in this paper. Both the twin-core couplers as well as the multiple-core couplers are considered here in this paper. The parameter dynamics of the solitons that are governed by the coupled generalized nonlinear Schrodinger's equation, due to non-Kerr law nonlinearity, has been obtained for such couplers. [ABSTRACT FROM AUTHOR]

The variational principle is employed to obtain the evolution of the parameters of a super-Gaussian chirped soliton that propagates through an optical fiber and is governed by the dispersion-managed nonlinear Schrödinger's equation. These pulses have better features compared to a classical soliton and reduced timing jitter due to the Gordon-Haus effect. The waveform deviates from that of a classical soliton. The periodically-changing strong chirp of such a soliton reduces the effective nonlinearity that is necessary for balancing the local dispersion. This study is extended to obtain the adiabatic evolution of the parameters of such a soliton in the presence of perturbation terms. [ABSTRACT FROM AUTHOR]

The variational principle is employed to obtain the evolution of the parameters of Gaussian and super-Gaussian chirped solitons that propagates through multiple-core nonlinear optical fiber arrays. This is governed by the dispersion-managed nonlinear Schrödinger's equation with strong dispersion management in the presence of linear coupling between the adjacent cores. The results are valid for any configuration of the cores. [ABSTRACT FROM AUTHOR]

The existence of a dynamically stable soliton in optical fibers is established by virtue of the multiple-scale perturbation technique applied in a new way to the perturbed nonlinear Schrödinger's equation. We show that, by introducing a proper definition of the phase of the soliton, one can obtain the corrections to the pulse where the standard soliton perturbation approach fails. [ABSTRACT FROM AUTHOR]