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Optical soliton solutions to the newly proposed Kudryashov's equation are obtained. The method of undetermined coefficients secured bright, dark and singular soliton solutions to the model. The conservation laws are also listed that are written in terms of Gauss' hypergeometric functions. Several parameter restrictions, that naturally emerged during the derivation process, are also enumerated. [ABSTRACT FROM AUTHOR]

A new model, namely Kudryashov's equation, for securing optical solitons has been proposed. This paper obtains bright and singular optical solitons to the equation by extended trial function. The existence criteria for such solitons are also enumerated. [ABSTRACT FROM AUTHOR]

This paper revisits Lakshmanan–Porsezian–Daniel model in birefringent fibers with five insightful integration algorithms. These schemes reveal bright, dark, singular and combo optical solitons to the model. Their respective existence criteria are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we employ four sound integration algorithms, namely three different auxiliary equation methods and a new extended generalized Kudryashov method to extract optical solitons and other solutions to coupled system of nonlinear Schrödinger's equations having anti-cubic nonlinearity in birefringent fibers without four wave mixing effects. Dark, bright, singular optical solitons and other solutions have thus emerged. [ABSTRACT FROM AUTHOR]

This paper secures, dark, singular and dark–singular combo optical soliton solutions to complex Ginzburg–Landau equation that is considered with three nonlinear forms. Two forms of integration architectures provide these solutions. • Optical solitons with complex Ginzburg-Landau equation is addressed. • Three distinct nonlinear forms of refractive index are studied. • Two forms of integration architectures are implemented. • Dark and singular solitons are revealed. [ABSTRACT FROM AUTHOR]

The dynamics of solitons, with newly modeled Kudryashov's equation, is revealed in this paper by the aid of F -expansion scheme. Thus, bright, dark and singular solitons emerged from it as well as complexiton solutions are presented. The sustaining criteria for the solitons are also enumerated. [ABSTRACT FROM AUTHOR]

This paper obtains highly dispersive perturbed bright 1-soliton solution with cubic–quintic–septic nonlinearity by the aid of semi-inverse variational principle. The relation between the parameters, for sustaining solitons, naturally emerge during the course of soliton solution derivation. [ABSTRACT FROM AUTHOR]

This paper establishes conservation laws, by Lie symmetry analysis, for highly dispersive optical solitons that have been studied with four nonlinear forms. Three conserved quantities reported are power, linear momentum and the Hamiltonian. These are recovered from soliton solutions established earlier. [ABSTRACT FROM AUTHOR]

In this paper, the art of semi-inverse variational principle is employed to retrieve highly dispersive bright optical solitons to the governing model, with perturbation terms, having Kerr nonlinearity. The existence criteria for these solitons are also chalked out. [ABSTRACT FROM AUTHOR]

This paper secures dispersive solitons in polarization-preserving fibers, birefringent fibers and DWDM networks. The extended simplest equation approach analyzes the governing Schrödinger–Hirota equation. A wide spectrum of soliton solutions is yielded. [ABSTRACT FROM AUTHOR]

This paper displays bright and singular optical solitons in fiber Bragg gratings with dispersive reflectivity for parabolic–nonlocal combo nonlinearity. The extended trial function approach is the integration scheme adopted in this paper. The existence criteria for such solitons are indicated. [ABSTRACT FROM AUTHOR]

This paper secured bright and singular soliton solutions to optical fiber Bragg gratings that is considered with cubic–quintic–septic form of nonlinear medium. The extended trial function scheme retrieves such soliton solutions. The existence criteria of these solitons are also presented. [ABSTRACT FROM AUTHOR]

This paper reports highly dispersive singular optical solitons with Kerr law nonlinearity. Jacobi's elliptic function expansion approach, with respect to ds function, revealed such soliton solutions. The existence criteria of such solitons are enlisted. [ABSTRACT FROM AUTHOR]

This paper obtains dark and singular 1-soliton solutions to birefringent fibers that is modeled by Lakshmanan–Porsezian–Daniel model. The adopted scheme is modified simple equation method. The integrability criteria for the governing model are also presented. [ABSTRACT FROM AUTHOR]

The extended trial function scheme is applied to retrieve soliton solutions to the perturbed nonlinear Schrödinger's equation with ten forms of fiber nonlinearity. Bright, dark and singular soliton solutions are retrieved that appear with their respective existence criteria. Some additional forms of nonlinear waves naturally emerge as a byproduct of the integration scheme. [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 reveals bright, dark and singular soliton solutions to the perturbed Gerdjikov-Ivanov equation by the aid of extended Kudryashov’s method. The nonlinear terms appear with full nonlinearity in order to give a generalized flavor to the model. As a byproduct of this scheme, plane waves and singular periodic solutions fall out and these solutions are listed as well. [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 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., (© 2019 The Authors. Published by Elsevier B.V. on behalf of Cairo University.)