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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]

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]

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]

This work studies cubic–quartic optical solitons with Kudryashov's law of refractive index. The extended trial function approach reveals solutions to the model in terms of Jacobi's elliptic functions that yields bright and singular optical solitons with limiting values to the modulus of ellipticity. The conservation laws are also presented. [ABSTRACT FROM AUTHOR]

This work recovers cubic–quartic soliton solutions to the Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Both polarization-preserving fibers and birefringent fibers are studied. The conservation laws for polarization-preserving fibers are also retrieved and enumerated. The existence criteria for the displayed solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies polarized cubic–quartic solitons that are modeled by Fokas–Lenells equation in birefringent fibers. Two integration schemes recovered a spectrum of soliton solutions to the model. Subsequently, the bright solitons compute the corresponding conserved quantities from the respective densities that are recovered by the multiplier approach. [ABSTRACT FROM AUTHOR]

This paper obtains the bright, singular and combo solitons solutions in birefringent fibers, with four-wave mixing, that maintains quadratic-cubic law of refractive of refractive index, by implementing traveling wave hypothesis. Adomian decomposition method is subsequently applied to the obtained results on bright solitons to display its numerical simulation with an impressive error measure. [ABSTRACT FROM AUTHOR]

This paper implements the sub-ODE method and a wide spectrum of solitons are recovered for Kudryashov's law of refractive index. The self-phase modulation comprises of four nonlinear components of refractive index. The perturbation terms are all of Hamiltonian type and are considered with maximum intensity. The solutions are written in terms of Weierstrass' elliptic functions and Jacobi's elliptic function. With the modulus of ellipticity approaching zero or unity, soliton solutions emerge. [ABSTRACT FROM AUTHOR]

This paper implements mathematically rigorous extended trial function algorithm to address cubic–quartic optical solitons in birefringent fibers having Kudryashov's law of nonlinear refractive index. Three special cases of the power-law nonlinearity parameter are taken into consideration. Bright and singular optical solitons emerge from this analytical scheme. [ABSTRACT FROM AUTHOR]

This paper studies couplers in optical metamaterials that come with power law of nonlinear refractive index. The Kudryashov's approach reveals bright, singular as well as bright-singular straddled optical soliton solutions. Both twin-core couplers and multiple-core couplers are studied. [ABSTRACT FROM AUTHOR]

This paper retrieves soliton solutions to fiber Bragg ratings with dispersive reflectivity where cubic–quartic dispersive effects are considered as opposed to the usual chromatic dispersion. The auxiliary equation approach and an addendum to Kudryashov's scheme display a complete spectrum of soliton forms to the model that is studied with Kerr effect. [ABSTRACT FROM AUTHOR]

Considering the self-steepening effect in a metamaterial (MM) can significantly change its behaviour. We study the propagation of ultrashort pulses in nonlinear MMs that is governed by a generalized nonlinear Schrö dinger equation with higher order effects such as pseudo-quintic nonlinearity and self-steepening effect. A class of chirped quasi-soliton solutions is obtained in the presence of the self-steepening term, and some of which are derived for the first time. The solutions comprise chirped bright quasi-solitons on a constant and zero background, kink and anti-kink quasi-solitons, and double-kink quasi-solitons. It is found that the nonlinear chirp associated with each of these waves is directly proportional to the intensity and its amplitude can be controlled by selecting the self-steepening and dispersion coefficients. Particular cases of chirp-free quasi-solitons are discussed. The conditions on MM parameters for the formation of these structures are also presented. The obtained results are important to explore much richer localized light pulses in MMs. [ABSTRACT FROM AUTHOR]

This paper obtains bright optical soliton solutions from resonant nonlinear Schrödinger’s equation by the aid of semi-inverse variational principle. The two forms of nonlinear media studied are parabolic and dual-power law. The necessary constraints 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 obtains soliton solutions in optical couplers. The governing equation is solved by the aid of G′/G-expansion scheme. There are four types of nonlinear media that are taken into consideration. These are Kerr law, power law, parabolic law, and dual-power law. There are two kinds optical couplers studied in this paper. They are twin-core couplers and multiple-core couplers, where coupling with nearest neighbors as well as coupling with all neighbors are considered. Dark and singular soliton solutions are retrieved. These soliton solutions come with constraint conditions that must hold for the solitons to exist. [ABSTRACT FROM AUTHOR]

This work retrieves polarized optical soliton solutions for pulses in birefringent fibers that are modeled by the Lakshmanan–Porsezian–Daniel model. The unified approach recovers singular solitons only. This approach fails to retrieve the much needed bright and dark soliton solutions. These singular solitons exist with restricted parametric conditions that are also exhibited. • Soliton solutions to Lakshmanan–Porsezian–Daniel model with differential group delay are revealed. • Singular soliton solutions are recovered by the unified approach. • These singular solitons exist with restricted parametric conditions that are also exhibited. [ABSTRACT FROM AUTHOR]

This paper displays numerical simulation for bright and dark optical solitons that emerge from Fokas-Lenells equation which is studied in the context of dispersive solitons in polarization-preserving fibers. The Laplace-Adomian decomposition scheme is the numerical tool adopted in the paper. The numerical results, for bright and dark solitons, are expository and therefore supplement the analytical developments, thus far. [ABSTRACT FROM AUTHOR]

This paper employs two integration schemes to extract dark and singular optical soliton solutions to the coupled Fokas-Lenells equation that is studied in the context of polarization-mode dispersion fibers. The existence criteria for these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper adopts the extended trial equation method to handle optical nonlinear negative-index materials that come with anti-cubic nonlinearity. In presence of Hamiltonian perturbation terms, soliton solutions are obtained. These are bright and singular solitons only. However, some additional wave solutions are also emerged. [ABSTRACT FROM AUTHOR]

This paper obtains conservation laws for soliton propagating in birefringent optical fibers and magneto-optic waveguides. The special cases of Thirring solitons, cascaded systems are also included. The nonlinearity types considered in this paper are Kerr law and parabolic law. Some well established methods are used for the analysis and retrieval of conservation laws. [ABSTRACT FROM AUTHOR]

We study for the first time perturbed optical solitons modelled using a Sasa-Satsuma equation involving a multiplicative noise. Two integration schemes retrieve soliton solutions to this model, which are described using parametric constraints. [ABSTRACT FROM AUTHOR]

We reveal cubic--quartic optical solitons with quadratic--cubic nonlinearity for the first time. Both polarization-preserving and birefringent optical fibres are considered. The study is also extended to include the perturbation terms of Hamiltonian type. The integration algorithm adopted in the present work is the method of sine-Gordon equation. [ABSTRACT FROM AUTHOR]

For the first time in the field of nonlinear optics, we address cubic--quartic solitons appearing in the fibre Bragg gratings with dispersive reflectivity for four different cases of nonlinear refractive-index structures. A complete spectrum of single solitons, together with some straddled solitons, emerges from the integration scheme adopted by us, which is the approach of sine--Gordon equation. [ABSTRACT FROM AUTHOR]

We retrieve analytically a bright 1-soliton solution to a perturbed cubic-quartic Lakshmanan-Porsezian-Daniel model, using a semi-inverse variational principle. The perturbation terms are considered arising from the condition of maximum allowable intensity. The restrictions imposed by integrability considerations on the model parameters are enlisted. It is important that the other analytical approaches available fail to recover the analytical bright-soliton solution to the model with the maximum allowable intensity. [ABSTRACT FROM AUTHOR]

We study stationary optical solitons for the case of Lakshmanan-Porsezian-Daniel model with nonlinear chromatic dispersion and a Kerr law of nonlinear refractive index. The solution is expressed in terms of a special function and its structure is described in details. [ABSTRACT FROM AUTHOR]

We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov's sextic power-law nonlinearity of refractive index. Three different integration schemes have been implemented. These are a unified Riccati equation, our new mapping scheme and our addendum to the common N. A. Kudryashov's method. All of the solitons are enlisted and the criterions of their existence are mentioned. Finally, we extract three appropriate conservation laws. [ABSTRACT FROM AUTHOR]

Cubic-quartic soliton transmission having power law of nonlinearity refractive index. • Optical soliton solutions for the perturbed nonlinear Schrodinger's equation are revealed. • Quadratic-cubic nonlinearity is considered. • Bright optical solitons are retrieved by the help of the IADM. • The numerical results together with high level accuracy plots are exhibited. • The method proposed herein works with high degree of accuracy. This paper numerically retrieves cubic-quartic solitons having power law of nonlinearity refractive index. An improvement of the Adomian decomposition scheme is the adopted algorithm of this work. The results are displayed along with the established error analysis. [ABSTRACT FROM AUTHOR]

Highly dispersive optical solitons are obtained for nonlinear Schrödinger's equation that is studied in absence of self-phase modulation. The effect of nonlinearity comes from perturbation terms. Jacobi's elliptic function expansion reveals bright and dark soliton solutions to the model. [ABSTRACT FROM AUTHOR]

This paper studies optical solitons in birefringent fibers with anti-cubic nonlinearity. The exp-function scheme retrieves singular and combo solitons. The existence criteria for these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper studies highly dispersive optical solitons when self-phase modulation term is completely absent. The delicate balance for existence and sustaining of solitons is provided by self-steepening effect and nonlinear dispersions. The exp-function approach yields singular and bright-singular combo solitons. [ABSTRACT FROM AUTHOR]

This paper obtains highly dispersive singular optical solitons in cubic–quintic–septic nonlinear medium. The exp-function expansion is the applied integration algorithm. The solitons appear with their corresponding existence criteria. [ABSTRACT FROM AUTHOR]

This paper recovers singular and bright-singular highly dispersive optical solitons, having non-local form of nonlinearity, by the application of exp-function integration scheme. The existence criteria for these solitons are also listed in the work. [ABSTRACT FROM AUTHOR]

This paper studies highly dispersive optical solitons by the application of exponential function. The model is with quadratic–cubic nonlinear fibers. The algorithm reveals singular and bright–singular combo soliton solutions. The integrability criteria are also listed in this work. [ABSTRACT FROM AUTHOR]

This paper obtains bright and singular optical solitons that are studied with anti-cubic nonlinearity in birefringent fibers. The extended trial function scheme gave way to these results. The existence criteria of such solitons are also indicated. [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]

In this work, symmetry reduction for nonlinear Schrödinger's equation with anti-cubic nonlinearity is determined by using the invariance of equations under Lie group of transformations. Using the similarity transformations the equation is reduced into system of ordinary differential equations. Corresponding to reduced ordinary differential equations, some exact solutions are obtained. These yields bright solitons, dark solitons, singular solitons and other explicit solutions. It is also pointed out that some of the results reported earlier are particular forms of current solutions. [ABSTRACT FROM AUTHOR]

Optical soliton solutions are recovered for fibers having anti-cubic nonlinear law. Bright, dark and singular optical soliton solutions are retrieved by the aid of three forms of integrability tools. The existence criteria for such solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper secures bright optical solitons in presence of third and fourth order dispersion terms while group velocity dispersion term is absent. The perturbation terms that are included appear with full nonlinearity. The semi-inverse variational principle is implemented to secure such solutions. [ABSTRACT FROM AUTHOR]

This paper secures bright-singular combo highly dispersive optical solitons by the application of exponential-function method. Several other solutions also emerged from the scheme although they are not applicable in nonlinear optics. The solitons appear with their respective integrability criteria that are also presented in this work. [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]

The work on this paper focuses on the retrieval of highly dispersive optical solitons that maintain non-local nonlinearity. The extended version of Jacobi's elliptic function expansion successfully yielded bright and singular as well a couple of combo optical solitons. The parameter restrictions, for the existence of such solitons, naturally emerged from the scheme. [ABSTRACT FROM AUTHOR]

This work is about highly dispersive optical solitons with Kerr and power law nonlinearity. Bright, dark and singular solitons are obtained from undetermined coefficients. This method proves that highly dispersive optical solitons are obtainable only with inter-modal and group velocity dispersions for both nonlinear forms. [ABSTRACT FROM AUTHOR]

This paper successfully applied F -expansion algorithm to obtain highly dispersive optical solitons with cubic-quintic-septic nonlinearity. Bright, dark and singular solitons and their combinations thereof are listed. Their respective existence criteria are also indicated. Additional solutions such as periodic singular solutions as well as results in terms of Weierstrass elliptic function are also revealed from the scheme. [ABSTRACT FROM AUTHOR]

Optical soliton solutions are retrieved for Lakshmanan–Porsezian–Daniel equation by employing Riccati equation approach. The soiton solutions that are presented are generalized versions of solutions that have been reported in the past. The constraint conditions guarantee the existence of such solitons. [ABSTRACT FROM AUTHOR]

This paper retrieves soliton solutions to Kaup–Newell's equation in optical fibers. Two fundamental integration schemes, namely the csch-function method and traveling wave hypothesis, obtain singular and bright soliton solutions respectively. The existence criteria for these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper retrieves, bright, dark and singular highly dispersive optical solitons with quadratic-cubic law of nonlinearity. The F -expansion scheme is the integration algorithm adopted in the paper. There are other solutions to the model that are also recovered such as doubly periodic functions, Weierstrass elliptic functions and periodic solutions. [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]

Abstract We investigate the propagation of self-similar optical solitons on a continuous-wave background through a non-centrosymmetric waveguide with second- and third-order nonlinearities. The generalized inhomogeneous nonlinear Schrödinger equation with quadratic–cubic nonlinearities and gain or loss is used to describe the beam propagation through the waveguide. Three new types of exact self-similar localized solutions propagating on a continuous-wave background are found under certain parametric conditions. The self-similar wave solutions comprise bright solitons, W-shaped, and kink solitons. The dynamic behaviors of these solitons are analyzed for a periodically distributed dispersion system. Highlights • Self-similar optical solitons with continuous-wave background are studied. • The self-similar wave solutions comprise bright solitons, W-shaped, and kink solitons. • The dynamic behaviors of these solitons are analyzed. [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]