On weakly BR-closed functions between topological spaces

In this paper, we offer a new class of functions called weakly BR-closed functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already well-known functions

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

SUPER-SECH SOLITON DYNAMICS IN OPTICAL METAMATERIALS USING COLLECTIVE VARIABLES

This paper presents collective variable approach for super-sech soliton dynamics in optical metamaterials. The soliton dynamics is governed by the generalized nonlinear Schrödinger's equation. The numerical simulations of pulse width, amplitude, chirp and frequency are given

Conservation laws for perturbed solitons in optical metamaterials

The conservation laws for the dynamics of soliton propagation through optical metamaterials are derived by the aid of Lie symmetry analysis. The proposed model will be studied with two forms of nonlinearity. They are Kerr law and parabolic law.National Natural Science Foundation of China (NSFC) - 2015CFC891Department of Mathematics and Statistics at Tshwane University of TechnologySouth African National Foundation - 92052 IRF1202210126National Research Foundation of Korea Qatar National Research Fund (QNRF) - NPRP 8-028-1-00

W-shaped chirp free and chirped bright, dark solitons for perturbed nonlinear Schrödinger equation in nonlinear optical fibers

In the present investigation, we employed the Jacobi elliptic function (JEF) method to invoke the perturbed nonlinear Schrödinger equation with self-steepening (SS), self-phase modulation (SPM), and group velocity dispersion (GVD), which govern the propagation of solitonic pulses in optical fibres. The proposed algorithm proves the existence of the family of solitons in optical fibers. Consequently, chirped and chirp free W-shaped bright, dark soliton solutions are obtained from dn(ξ), cn(ξ) and sn(ξ) functions. The final results are displayed in three-dimensional plots with specific physical values of GVD, SPM and SS for an optical fiber

On the extension of classes of continuous maps to the bicompletion in quasi-uniform spaces

In [6] characterizations of continuous maps between uniform spaces in terms of nets and filters are provided. Also, extensions of maps defined on a dense subset of a uniform space that preserve Cauchy filterbases between uniform spaces to the whole space are discussed. It is the purpose of this paper to extend some of these results to the setting of quasi-uniform spaces, by discussing extensions of maps that preserve Cauchy filterbases between quasi-uniform spaces to the bicompletion. We also show that some results in [3]concerning extensions of quasi-uniformly continuous maps from T1-half completable quasi-uniform spaces also hold for maps that preserve Cauchy filterbases.Quaestiones Mathematicae 30(2007), 263{27

On completeness of quasi-pseudometric spaces

We discuss completeness in terms of a notion of absolute closure. This will be done in the context of separated quasi-pseudometric spaces and bitopological spaces. The notion is equivalent to the classical notion of completeness when restricted to the class of metric spaces. 1. Introduction an

On convergence completeness in symmetric spaces

The notion of a convergence complete symmetric space is introduced in [6]. In this paper we shall show that every symmetric space admits a weakly S-convergence complete symmetric space. As applications of convergence completeness, we present some fixed point results for self-maps defined on a symmetric space.Keywords: completeness; convergence completeness; fixed points; metric spaces; symmetric spacesQuaestiones Mathematicae 31(2008), 203–20

On completeness in symmetric spaces

In the literature completeness for symmetric spaces is done through the classical Cauchy criterion for metric spaces. However, unlike the situation in metric spaces a convergent sequence in a symmetric space is not necessarily a Cauchy sequence. In the paper we introduce a notion of convergence completeness for symmetric spaces and characterize completeness for these spaces without appealing to the notion of a Cauchy sequence. The new notion is equivalent to completeness when restricted to the class of metric spaces.Keywords: Completeness, convergence complete, extension of spaces, metric space, symmetric distance space.Quaestiones Mathematicae 30(2007), 13–2

Sub pico-second pulses in mono-mode optical fibers with Kaup–Newell equation by a couple of integration schemes

This paper examines soliton dynamics of sub pico-second pulses modeled by Kaup-Newell equation. The modified simple equation scheme and trial equation approach retrieves dark, bright as well as singular solitons to the model. The constraint relations guarantee the existence of such solitons