Seithuti P. Moshokoa

Nematicons in liquid crystals by extended trial equation method

This paper employs extended trial equation method to retrieve nematicons in liquid crystals from its governing equation. In addition, several other forms of solution naturally emerged from the integration algorithm. These are shock waves, singular solitons, snoidal waves, periodic singular waves, plane waves and others. These variety of solutions are being reported for the first time in the context of liquid crystals.

Resonant optical solitons with parabolic and dual-power laws by semi-inverse variational principle

Abstract 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.

Reduced differential transform method for partial differential equations within local fractional derivative operators

The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

Solitons in Nonlinear Directional Couplers with Optical Metamaterials by Trial Function Scheme

Solitons in Nonlinear Directional Couplers with Optical Metamaterials by Trial Function Scheme A.H. Arnous, M. Ekici, S.P. Moshokoa, M. Zaka Ullah, A. Biswasc,d∗and M. Belic Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk, Cairo, Egypt Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box-80203, Jeddah-21589, Saudi Arabia Science Program, Texas A&M University at Qatar, P.O. Box 23874, Doha, Qatar

Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators

The local fractional Laplace variational iteration method (LFLVIM) is employed to handle the diffusion and wave equations on Cantor set. The operators are taken in the local sense. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

Homotopy Perturbation Method to Obtain Positive Solutions of Nonlinear Boundary Value Problems of Fractional Order

We use the homotopy perturbation method for solving the fractional nonlinear two-point boundary value problem. The obtained results by the homotopy perturbation method are then compared with the Adomian decomposition method. We solve the fractional Bratu-type problem as an illustrative example.

Chirped bright and double-kinked quasi-solitons in optical metamaterials with self-steepening nonlinearity

ABSTRACT 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.