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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]

Propagating chirped soliton solutions for the Chen–Lee–Liu equation also called the derivative nonlinear Schrödinger II equation are investigated by application of the ansatz method. The model incorporating self-steepening term has many applications in nonlinear optical fibers and plasma physics. A nonlinear differential equation describing the evolution of the wave amplitude in the nonlinear media is derived by means of the coupled amplitude-phase formulation. Special exact chirped soliton solution that takes the shape of “ W ” is determined for the first time in presence of all physical effects. It is shown that the nonlinear chirp associated with this type of solitons is crucially dependent on the wave intensity and related to self-steepening and group velocity dispersion parameters. Parametric conditions on system parameters for the existence of the chirped soliton structure are also presented. This soliton solution exists due to a balance among group velocity dispersion and self-steepening effect solely. [ABSTRACT FROM AUTHOR]

We consider the evolution of ultrashort pulses in metamaterials wherein the pulse propagation is governed by the generalized nonlinear Schrödinger equation with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. We present three new types of exact singular soliton-like solutions for the model in the presence of the self-steepening term, whose phase chirping varies as a function of the pulse intensity. The obtained results indicate that the parameters of solutions are directly related the self-steepening parameter. Parametric conditions on physical parameters for the existence of the novel structures are also presented. Particular cases are discussed. [ABSTRACT FROM AUTHOR]

This paper derives bright 1-soliton solution to the resonant nonlinear Schrödinger's equation that is studied with anti-cubic nonlinearity. The semi-inverse variational principle is adopted to secure analytical solution to the model. The parametric restrictions that emerge for the existence of solitons are also presented. [ABSTRACT FROM AUTHOR]

Abstract In this paper, to build soliton solutions of the governing equation, describing a propagation of sub-picosecond pulses with cubic-quintic nonlinearity and fourth-order dispersion in optical fibers, we use three methods: auxiliary equation, sine-cosine method and csch function method. The results obtained are 1-soliton solutions that propagate in the fiber optic and LHMs. [ABSTRACT FROM AUTHOR]

Abstract This paper retrieves chirped singular and bright-singular combo optical soliton solutions to the Chen–Lee–Liu equation. Three forms of independent intregration schemes are implemented to the model. They are csch function scheme, tanh–coth method and finally the modified simple equation approach. The integrability criteria for these are also presented. [ABSTRACT FROM AUTHOR]

Abstract We investigate the Kaup-Newell equation that represents one of the forms of derivative nonlinear Schrödinger equation. The model applies to the description of sub-pico-second pulse propagation through an optical fiber. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describing the dynamics of field amplitude in the nonlinear media. It is shown that the phase associated to the obtained pulses has a nontrivial form and possesses two intensity dependent chirping terms in addition to the simplest linear contribution. A class of soliton solutions of the bright, dark and singular type are derived for the first time. The requirements concerning the optical material parameters for the existence of these chirped structures are also discussed. [ABSTRACT FROM AUTHOR]

In this study, soliton solutions with differential group delay, having parabolic law nonlinearity, are constructed. The exp(− ϕ ( ξ ))-expansion method has been utilized. Additional solutions, including plane wave solutions and periodic singular waves naturally emerge from the integration scheme. [ABSTRACT FROM AUTHOR]

This study carries out the integration of Gerdjikov–Ivanov equation. The csch method, the extended tanh–coth method, and the modified simple equation method are utilized to extract the analytical soliton solutions. [ABSTRACT FROM AUTHOR]

This paper obtains bright, dark, singular and other combo optical soliton solutions to perturbed Kaup–Newell equation. Two strategic integration schemes are fruitfully applied to obtain these solutions. These solitons appear with constraint conditions on the soliton parameters that are also presented. [ABSTRACT FROM AUTHOR]

This paper reveals dark and singular optical solitons, as well as their combinations thereof, of the perturbed Kundu–Eckhaus equation. Two integration methodologies are adopted here. The existence criteria for these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper employs dextended Jacobi's elliptic function expansion method to retrieve doubly periodic function as solutions to the stochastic complex Ginzburg–Landau equation. In the limiting case, when the modulus of ellipticity approaches unity, these solutions approach optical solitons. This paper lists the dark-singular combo optical solitons. [ABSTRACT FROM AUTHOR]

This paper obtains bright, dark and singular optical soliton solutions to the Lakshmanan–Porsezian–Daniel model that describes soliton propagation through polarization-mode dispersive fibers, without the effect of four-wave mixing. The method of undetermined coefficients is employed to retrieve these soliton solutions. The existence criteria for these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies optical solitons in birefringent fibers by the aid of exp-function approach. The model that is analyzed is Lakshmanan–Porsezian–Daniel equation which is first written in two-component form for vector solitons. The integrability criteria are also presented in the paper. [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 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 secures dark and singular resonant optical solitons that is studied with dual-power law nonlinearity and fractional temporal evolution. Khalil's conformable fractional derivative is put into perspective to retrieve these soliton solutions. The parameter restrictions for the existence of such solitons are also indicated. [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]

This paper obtained singular and dark-singular combo solitons to Fokas–Lenells equation by the aid of traveling wave hypothesis. The modified simple equation scheme retrieved plane wave solutions to the model. The existence criteria of these waves are also presented. [ABSTRACT FROM AUTHOR]

The dynamics of pulse propagation through nonlinear optical metamaterials, maintaining parabolic law nonlinearity, is investigated. The model includes spatio-temporal dispersion, detuning effect, inter-modal dispersion, self-steepening effect, Raman scattering, nonlinear dispersion and third-order dispersion. Bright, dark and singular soliton solutions are derived by the implementation of coupled phase-amplitude formulation. The conditions on the material parameters for the existence of these solitons are also enumerated. [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 retrieves optical soliton solutions in a parabolic law medium that also comes with weak nonlocal nonlinearity. The extended trial function method secures bright and singular soliton solutions to the model. In addition, plane waves and snoidal wave solutions also emerge naturally from this integration scheme. [ABSTRACT FROM AUTHOR]

This paper obtains optical soliton solutions to the perturbed Radhakrishnan–Kundu–Lakshmanan equation by trial equation method and modified simple equation algorithm. There are two types of nonlinear fibers studied in this paper. They are Kerr law and power law. Bright, dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration schemes. [ABSTRACT FROM AUTHOR]

This paper conducts Lie group analysis of the perturbed Radhakrishnan–Kundu–Lakshmanan equation to retrieve optical soliton solutions. This powerful integration scheme retrieves bright and dark optical soliton solutions to the model that is studied with power law nonlinearity. The existence criteria of such solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper implements modified direct algebraic method to secure soliton solutions in quadratic-cubic medium. Bright and dark-singular combo solitons are obtained along with their existence criteria. Several other solutions to the model including periodic singular solutions are also presented. [ABSTRACT FROM AUTHOR]

This paper retrieves bright, dark and singular optical solitons in birefringent fibers using two integration schemes. They are trial equation method and modified simple equation scheme. Bright, dark and singular soliton solutions are revealed using these integration schemes. Additional solutions such as periodic singular waves also naturally emerge from these methodologies. [ABSTRACT FROM AUTHOR]

This paper obtains bright, dark and singular dispersive optical soliton solutions to Schrödinger–Hirota equation by the aid of trial equation method. Both Kerr and power laws of nonlinearity are studied. Singular periodic solutions are also obtained as a byproduct of this scheme. [ABSTRACT FROM AUTHOR]

This paper obtains bright and dark–singular combo solitons for the Lakshmanan–Porsezian–Daniel model by the aid of modified extended direct algebraic method. Both Kerr law and power law nonlinearities are considered. However, it is only the case of Kerr law that led to soliton solutions. Some additional solutions also emerged and they are singular periodic waves and elliptic functions. [ABSTRACT FROM AUTHOR]

This paper obtains bright and dark-singular combo optical solitons in a parabolic law medium that is coupled with weak non-local nonlinearity. The method of modified extended direct algebraic method is applied to secure these soliton solutions. Additionally, several other solutions in terms of elliptic functions naturally fall out of the integration scheme as a byproduct. [ABSTRACT FROM AUTHOR]

This paper secures optical solitons with fractional temporal evolution in presence of a few perturbation terms. The extended G ′/ G -expansion method reveals bright, dark and singular soliton solutions to the model. The study is conducted with four forms of nonlinear media. The results will be useful to conduct slow evolution of pulses in an optical fiber for controlling Internet bottleneck. [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]

This paper secures bright, dark and singualr soliton solutions in birefringent fibers. Both Kerr law and parabolic law nonlinearity are studied. The trial equation method successfully retrieves these solitons with constraint relations that assure their existence. [ABSTRACT FROM AUTHOR]

This paper retrieves soliton solutions to the perturbed resonant nonlinear Schrödinger's equation with time-dependent coefficients using the modified simple equation method. The four types of exotic non-Kerr laws studied in this paper are quadratic–cubic law, anti-cubic law, cubic–quintic–septic law and triple-power law. These soliton solutions appear with constraint conditions that guarantee their existence. [ABSTRACT FROM AUTHOR]

This paper retrieves optical soliton solution to the perturbed complex Ginzburg–Landau equation that is studied with nine different forms of nonlinearity. The trial solutions approach is the integration algorithm adopted in this paper. The perturbation terms appear with full nonlinearity to get a taste of generalized setting. Bright, dark and singular soliton solutions are obtained. The existence criteria of such solitons are also presented. [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]

The dynamics of soliton propagation through optical fibers, modeled by perturbed Kundu–Eckhaus equation, is studied in this paper by the aid of extended trial function scheme. The perturbation terms are all of Hamiltonian type that appears with full nonlinearity. Bright and singular soliton solutions are secured with this integration scheme. [ABSTRACT FROM AUTHOR]

The soliton solutions are extracted from the Lakshmanan–Porsezian–Daniel model by the aid of modified simple equation method. There are three forms of fibers that are studied and they represent Kerr law, parabolic law and anti-cubic law. The implementation of the scheme yields dark and singular soliton solutions to the model. The constraint conditions hold these solitons in place. [ABSTRACT FROM AUTHOR]

This paper retrieves dispersive optical soliton solutions to Schrödinger-Hirota equation in birefringent fibesr that models dispersive optical soliton propagation. The extended trial equation method is the integration algorithm employed here. Bright and singular solitons solutions are obtained along with other forms of solutions such as snoidal waves and singular periodic solutions. [ABSTRACT FROM AUTHOR]

This paper retrieves dark and singular optical soliton solutions to the Lakshmanan–Porsezian–Daniel equation for Kerr law nonlinearity by using two integration schemes. These are extended Jacobi's elliptic function approach and exp(−Φ( η ))–expansion method. The existence criteria for these solitons are also obtained that are presented as constraint conditions. As a byproduct, periodic singular solutions are recovered and these too are listed in the paper. [ABSTRACT FROM AUTHOR]

This paper obtains bright and singular optical soliton solutions to perturbed Gerdjikov–Ivanov equation by the aid of extended trial equation method. This work is an extension of the previously reported results where unperturbed version of the model was addressed. The results collapse to their prior versions upon turning off the perturbations. [ABSTRACT FROM AUTHOR]

The modified simple equation method applied to perturbed complex Ginzburg–Landau equation gives dark and singular solutions to the model. The perturbation terms appear with full nonlinearity. There are eight nonlinear forms studied in this paper. These solitons appear with constraint conditions that gurantee its existence and these are also presented. [ABSTRACT FROM AUTHOR]

The modified simple equation scheme is employed to secure dark and singular optical soliton solution to the perturbed Gerdjikov–Ivanov equation that models pulse dynamics in optical fibers and PCF. The solvability conditions for this algorithm is also presented. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of soliton propagation through optical fibers and PCF that are governed by Gerdjikov–Ivanov equation. The extended trial function approach is the integration scheme that is employed in this paper. There are bright and singular optical soliton solutions retrieved. The existence condition for these solitons is also presented. [ABSTRACT FROM AUTHOR]

This paper obtains optical soliton solution to perturbed Gerdjikov–Ivanov equation by trial equation approach. Bright, dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also emerge of this integration scheme. [ABSTRACT FROM AUTHOR]

This paper studies optical soliton perturbation with spatio-temporal dispersion by trial equation method. There are five types of nonlinear fibers studied in this paper. They are quadratic-cubic law, anti-cubic law, cubic-quintic-septic law, triple-power law and log-law. Bright, dark and singular soliton solutions are recovered. In addition, singular periodic solutions naturally emerge as a byproduct of this integration mechanism. [ABSTRACT FROM AUTHOR]

This paper secures dark and singular optical soliton solution to the perturbed Kundu–Eckhaus equation where the perturbation terms appear with full nonlinearity. The integration algorithm adopted in this paper is the modified simple equation approach. The solitons appear with certain parameter restrictions that are listed as constraints. [ABSTRACT FROM AUTHOR]

This paper obtains optical soliton solutions to the Kundu–Eckhaus equation with general coefficients. The Riccati–Bernoulli's sub-ODE method as well as Kudryashov's scheme are employed to obtain soliton solutions to the model. This generalized earlier reported result of the model with specific coefficients. Subsequently, the multiplier approach was utilized to secure a conserved quantity with the bright soliton solution that was reported earlier. [ABSTRACT FROM AUTHOR]

This paper obtains resonant soliton solutions to the nonlinear Schrödinger's equation that is studied in quadratic-cubic nonlinear media. The semi-inverse variational principle is applied to retrieve the soliton solution. The soliton parameters appear with restrictions that are also presented. [ABSTRACT FROM AUTHOR]