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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 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 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 This paper retrieves dark and singular optical solitons in birefringent fibers that is modeled by Kundu–Eckhaus equation. The most fundamental principle of undetermined coefficients is the extraction algorithm applied to the model. These solitons appear with integrability criteria that are also presented. [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 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]

Abstract: This paper addresses the dynamics of solitons in optical metamaterials. Both bright and dark soliton solutions are obtained. The ansatz method of integration is employed to extract the 1-soliton solutions to the governing equations. A couple of constraint relations are obtained in order for these solitons to exist. A few numerical simulations are also given to expose the dissipative effects. [Copyright &y& Elsevier]

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 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 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 studies the resonant optical solitons that comes with anti-cubic nonlinearity in presence of Hamiltonian perturbation terms. The extended trial function method is employed to retrieve cnoidal waves, bright and singular soliton solutions as well as periodic singular solutions to the model. [ABSTRACT FROM AUTHOR]

This paper obtains optical soliton solutions to the Lakshmanan–Porsezian–Daniel model. The method of undetermined coefficients is applied to extract these solutions. Bright, dark and singular soliton solutions are obtained and the constraint conditions for the existence of these solitons are presented. [ABSTRACT FROM AUTHOR]

This paper studies the dynamics of soliton propagation through optical metamaterials. The proposed model will be studied with five forms of nonlinearity. They are Kerr law, power law, parabolic law, dual-power law and log-law. The integration scheme that will be adopted is the method of undetermined coefficients. Bright, dark and singular soliton solutions will be obtained. The essential conditions for the existence of these solitons will naturally emerge. [ABSTRACT FROM AUTHOR]

This paper studies the propagation of solitons through birefringent fibers in the presence of spatio-temporal dispersion. Both Kerr and parabolic laws of nonlinearity are addressed. The exact 1-soliton solutions are obtained. There are several constraint conditions that ensure soliton solutions are derived. Three types of solitons are obtained: bright, dark and singular solitons. [ABSTRACT FROM AUTHOR]

This paper studies the perturbed optical solitons with parabolic and dual-power law nonlinearities in presence of spatio-temporal dispersion. The semi-inverse variational principle is applied to extract an analytical 1-soliton solution to the governing equation. There are constraint conditions that naturally fall out for the existence of these solitons. [ABSTRACT FROM AUTHOR]