Solitons for perturbed Gerdjikov–Ivanov equation in optical fibers and PCF by extended Kudryashov’s method

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.     

Optical Soliton Perturbation with Generalized Quadratic–Cubic Nonlinearity by Semi-Inverse Variation

Optics and Spectroscopy - The current work recovers a perturbed bright 1-soliton solution to the governing model that maintains generalized quadratic–cubic nonlinearity. The perturbation...     

Solitons in nonlinear directional couplers with optical metamaterials

This paper obtains bright, dark, and singular optical solitons in nonlinear directional couplers with optical metamaterials. The mathematical principle of undetermined coefficients is applied to extract these soliton solutions, with phase-matching condition. The constraint conditions for the existence of soliton solutions naturally emerge from the solutions. Both twin-core couplers and multiple-core couplers are studied in this paper.

     

Optical solitons in nonlinear directional couplers with trial function scheme

Nonlinear Dynamics - This paper obtains bright, dark and singular soliton solutions to optical couplers that appear with four forms of nonlinearity. Twin-core couplers as well as multiple-core...     

Optical soliton perturbation for Gerdjikov–Ivanov equation via two analytical techniques

This paper employs two integration procedures to obtain soliton solutions to the perturbed Gerdjikov–Ivanov equation. They are G′/G²–expansion method and the sine–cosine method. Bright, dark and singular solitons are revealed along with a few of the combo–soliton solutions. The existence criteria of these solitons are also given.     

Strongly (λ, θ)-continuous functions

In the paper, we introduce and investigate basic properties of a new class of functions between topological spaces called strongly (λ, θ)-continuous functions which is stronger than λ-continuous functions. This work was completed while the second author was visiting the Department of Mathematical Sciences, Unisa, Pretoria, South Africa partially supported by the National Research Foundation of South Africa.     

Nematicons in liquid crystals by modified simple equation method

Nonlinear Dynamics - This paper obtains nematicon solutions in liquid crystals by the aid of modified simple equation method. There are four types of nonlinearity studied. They are cubic law, power...     

Optical soliton perturbation with quadratic-cubic nonlinearity using a couple of strategic algorithms

In this work, we derive bright, dark and singular soliton solutions to quadratic-cubic nonlinear media with perturbation terms being present. We perform the modified simple and the trial equation algorithms to the considered model. In addition, periodic singular wave solutions will be constructed by the integration schemes.