Seithuti Moshokoa

Tshwane University of Technology | tut · Department of Mathematics and Statisctics

The enhanced Kudryashov’s approach retrieves quiescent bright, dark, and singular solitons to the governing model that is considered with cubic–quartic form of self-phase modulation. The algorithm however fails to retrieve stationary solitons when the nonlinearity is the generalized version of the cubic–quartic form. The current analysis is conduct...

This paper obtains soliton solutions to Sasa–Satsuma equation, which is studied in birefringent fibers with multiplicative noise. The extended auxiliary equation approach reveals solutions in terms of Jacobi’s elliptic functions from which bright, dark and singular solitons emerge when the limiting operation is applied to the modulus of ellipticity...

The current work recovers a perturbed bright 1.soliton solution to the governing model that maintains generalized quadratic--cubic nonlinearity. The perturbation terms appear with full intensity. The semiinverse variational principle secures this soliton when all of the known approaches fail, in this regard. Key words: solitons; quadratic.cubic; se...

A single bright highly dispersive optical soliton solution is recovered from semi–inverse variational principle. The model contains six power law nonlinear terms that constitute self–phase modulation effect which was proposed by Kudryashov. The amplitude–width relation of the soliton was finally recovered by Cardano’s approach with appropriate and...

This paper recovers cubic–quartic optical solitons for perturbed Fokas–Lennels equation in polarization–preserving fibers and birefringent fibers. The perturbation terms appear with maximum permissible intensity. Singular and dark solitons, together with a few combo solitons, emerge from the sine–Gordon equation integration scheme.

In this paper, A deterministic for top five medical insurance in South African market system is analyzed under important parameters such as emigration, immigration, personal interaction and advertisement. The critical outcome indicate all those medical insurance will remain relevant to South African population as long the aforesaid parameters are p...

In recent years, mathematical models have been developed to illustrate some physical phenomena in science and engineering. One of those systems of nonlinear differential equations is Brusselator chemical model. A mathematical template of checking accuracy of from black-boxes has been developed and investigated. Brusselator model is used as case stu...

In this paper, A model for the four major South African banks namely Absa, First national, Standard and Nedbank users is developed and investigated. Series solutions for South African banks users is obtained using the Adomian decomposition method under factors emigration, immigration , advertisement of each bank and personal interaction amongst dif...

This paper applies new ϕ6 model expansion scheme to obtain solitons in magneto–optic waveguides that come with dual–power law nonlinearity. Initially, the solutions are in terms of Jacobi's elliptic functions. Upon approaching the limiting values of the modulus of ellipticity, bright, dark and singular solitons emerge. The existence criteria of suc...

This paper studies perturbed Chen–Lee–Liu equation where the perturbation terms are with full nonlinearity. Seven integration algorithms reveal bright, dark, singular as well as combo–singular solitons to the model. The existence criteria of such solitons are also enumerated.

This paper retrieves stationary optical solitons to Sasa–Satsuma equation that carries nonlinear chromatic dispersion. The solutions are in terms of Gauss' hypergeometric functions and consequently the convergence criteria are also listed.

In this paper, we introduce a new class of functions between topo- logical spaces, namely almost lambda-continuous functions and present some properties for these functions.

In the paper [5], Moshokoa introduced the concept of slightly λ-continuous functions. It is purpose of this paper to investigate basic properties of slightly λ-continuous functions and introduce the relationships between these functions and separation axioms, graphs and compactness

This work investigate, An idea of checking accuracy of algorithms from mathematical black box by means of residual functions. Lorenz system is used as case study as the chaotic system does not have analytical solution. The numerical procedures examined include BDF, Adams method and Implicit Runge Kutta methods. The interval of numerical results is...

We investigate a generalized nonlinear Schrödinger equation with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. The model applies to the description of ultrashort pulse propagation in nonlinear materials exhibiting a negative index of refraction. Three new types of nonlinearly chirped W-shaped soliton solutions...

This paper examine, a developed framework of testing the accuracy of built-in function from Mathcad software. The built-in functions tested includes Bulirsch-Stoer, Adams-Backward differential formula and Runge-Kutta4 adapt methods.

Optical soliton solutions are retrieved for Lakshmanan–Porsezian–Daniel equation by employing Riccati equation approach. The soiton solutions that are presented are generalized versions of solutions that have been reported in the past. The constraint conditions guarantee the existence of such solitons.

This paper retrieves soliton solutions to Kaup–Newell's equation in optical fibers. Two fundamental integration schemes, namely the csch-function method and traveling wave hypothesis, obtain singular and bright soliton solutions respectively. The existence criteria for these solitons are also presented.

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.

This paper studies coupled Fokas–Lenells equation that governs the dynamics of dispersive optical solitons in birefringent fibers. Lie symmetry analysis retrieved several solutions along with conservation laws. The conserved quantities are finally computed using the bright soliton solution reported earlier.

This paper secures bright optical solitons in presence of third and fourth order dispersion terms while group velocity dispersion term is absent. The perturbation terms that are included appear with full nonlinearity. The semi-inverse variational principle is implemented to secure such solutions.

In this work, symmetry reduction for nonlinear Schrödinger's equation with anti-cubic nonlinearity is determined by using the invariance of equations under Lie group of transformations. Using the similarity transformations the equation is reduced into system of ordinary differential equations. Corresponding to reduced ordinary differential equation...

Optical soliton solutions are recovered for fibers having anti-cubic nonlinear law. Bright, dark and singular optical soliton solutions are retrieved by the aid of three forms of integrability tools. The existence criteria for such solitons are also presented.

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.

This work studies fractional temporal evolution of oblique resonant optical solitons in (3+1)-dimensions with Kerr- and parabolic-law nonlinearities. The generalized exp(−Φ(ξ))-expansion method along with the Khalil's conformable fractional derivatives is implemented to locate several forms of oblique resonant solitons. It is observed that obliquen...

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.

We investigate the propagation of self-similar optical solitons on a continuous-wave background through a non-centrosymmetric waveguide with second- and third-order nonlinearities. The generalized inhomogeneous nonlinear Schrödinger equation with quadratic–cubic nonlinearities and gain or loss is used to describe the beam propagation through the wa...

This paper conducts numerical studies of optical solitons with Lakshmanan–Porsezian–Daniel model having spatio-temporal dispersion. A newly proposed version of the well-known Adomian's decomposition method is applied to secure numerical simulations of the recently reported analytical soliton solutions. The focus of this paper stays with bright soli...

This research work presents some numerical the results and analyses of three types of bright soliton solutions for the Chen-Lee-Liu (CLL) equation obtained from the improved Adomian decomposition method. The error analyses of the algorithm ae also discussed.

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.

This paper obtains bright, dark and bright–dark combo cubic–quartic optical solitons when group velocity dispersion is negligible or totally absent. The model is studied with fractional temporal evolution by F-expansion scheme with Kerr and parabolic laws of nonlinearity. The results can be used to achieve slow-light dynamics thus enabling the cont...

This paper employs modified extended direct algebraic method to recover bright, dark and singular solitons for resonant nonlinear Schrödinger's equation that is studied with dual-power law media. Singular periodic solutions also emerge as a byproduct of this integration scheme.

In this paper we obtain soliton solutions to chiral nonlinear Schrödinger’s equation with the Bohm potential by the modified simple equation method and trial equation method. Solitons and shock wave solutions are obtained. Additionally, singular periodic solutions are revealed as a by-product of these approaches and these are also listed. The exist...

This paper studies solitons in optical couplers that are made up from metamaterials. Twin core as well as multiple-core couplers are considered. The study is conducted by the aid of exp(− Φ(ξ))-expansion scheme for four forms of nonlinearity and they are Kerr law, power law, parabolic law and dual-power law. Singular and combo-soliton solutions are...

In this paper, to build soliton solutions of the governing equation, describing a propagation of sub-picosecond pulses with cubic-quintic nonlinearity and fourth-order dispersion in optical fibers, we use three methods: auxiliary equation, sine-cosine method and csch function method. The results obtained are 1-soliton solutions that propagate in th...

This paper retrieves optical solitons in birefringent fibers having non-local nonlinearity in presence of four-wave mixing. Phase-matching conditions have been implemented to display these solitons. Bright, dark and singular soliton solutions are revealed.

The presence of inhomogeneities in an optical nonlinear material may significantly change the physical features of propagating envelopes. In this paper, we discuss the propagation of very short pulses in an inhomogeneous highly nonlinear single-mode fiber within the context of a higher-order nonlinear Schrödinger equation exhibiting a diversity of...

This paper retrieves mean free velocity of optical Gaussons that travel with stochastic perturbation in addition to bandpass filters and multi-photon absorption. The Langevin equation is derived and analyzed to arrive at the velocity in the limiting case.

This paper retrieves chirped singular and bright-singular combo optical soliton solutions to the Chen–Lee–Liu equation. Three forms of independent intregration schemes are implemented to the model. They are csch function scheme, tanh–coth method and finally the modified simple equation approach. The integrability criteria for these are also present...

This paper implements two efficient integration algorithms to retrieve soliton solutions that appear with weak nonlocal nonlinearity. These are trial equation method and modified simple equation scheme. Bright, dark and singular soliton solutions are recovered and their existence criteria are also presented.

This paper employs two strategic integration algorithms to extract soliton solutions to Kundu-Eckhaus equation in the context of birefringent fibers. The two schemes are G′/G²-expansion approach and sine-cosine method. Bright, singular and dark-singular combo solitons are retrieved. With reversed constraint conditions, singular-periodic solutions a...

The multiplier approach has been adopted to derive the conservation laws for optical solitons with non-local form of nonlinearity. The four conserved quantities are obtained from the 1-soliton solution that has already been reported earlier. The results are in terms of Gauss’ hypergeometric functions whose convergence criteria are compatible with t...

This paper obtains soliton solutions to perturbed Fokas-Lenells equation by the aid of exp-function approach. The perturbation terms are considered with full nonlinearity. Singular and combo-soliton solutions are presented along with their existence criteria.

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-soli...

We investigate the existence and stability properties of nonlinearly chirped solitary waves on a continuous-wave background in nonlinear metamaterials with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. Novel classes of chirped gray solitary pulses (dark pulses with nonzero minimum intensity) are derived by emp...

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.

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.

We investigate the Kaup-Newell equation that represents one of the forms of derivative nonlinear Schrödinger equation. The model applies to the description of sub-pico-second pulse propagation through an optical fiber. A special complex envelope traveling-wave method is applied to find a nonlinear equation with a fifth-degree nonlinear term describ...

Dark and bright with singular solitons shall be yielded to Fokas–Lenells equation which describes soliton dynamics in optical fibers. The two integration schemes that are applied in this context are the modified simple equation method and the trial equation method. Additional solutions, besides, optical solitons, are recovered.

This paper obtains conservation laws of Chen–Lee–Liu equation in optical fibers. The conserved densities are retrieved by Lie symmetry analysis and the conserved quantities are finally presented from bright 1-soliton solutions that are reported in the past.

In this paper, a mathematical framework of checking accuracy of built-in algorithms from Math-cad software is developed and investigated. The definite integral term obtained by reducing the Duffing equation from second order to first order differential equation is examined by three point Gauss quadrature rule. The selected built-in algorithms inclu...

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. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

This paper employs a couple of integration schemes to obtain soliton solutions in parabolic law medium with weak non–local nonlinearity. These are dark, singular and bright–singular combo solitons.

This paper secures dark and singular resonant optical solitons that is studied with dual–power law nonlinearity and fractional temporal evolution. Khalil’s conformable fractional derivative is put into perspective to retrieve these soliton solutions. The parameter restrictions for the existence of such solitons are also indicated.

This paper retrieves optical soliton solutions with fractional temporal evolution by the aid of generalized Kudryashov's method. There are four types of nonlinear fibers that are studied here. Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons are also presented.

This paper reveals dark and singular optical solitons, as well as their combinations thereof, of the perturbed Kundu–Eckhaus equation. Two integration methodologies are adopted here. The existence criteria for these solitons are also presented.

In this study, soliton solutions with differential group delay, having parabolic law nonlinearity, are constructed. The exp(−ϕ(ξ))-expansion method has been utilized. Additional solutions, including plane wave solutions and periodic singular waves naturally emerge from the integration scheme.

This paper studies optical solitons in birefringent fibers by the aid of exp-function approach. The model that is analyzed is Lakshmanan–Porsezian–Daniel equation which is first written in two-component form for vector solitons. The integrability criteria are also presented in the paper.

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 th...

This paper employs dextended Jacobi's elliptic function expansion method to retrieve doubly periodic function as solutions to the stochastic complex Ginzburg–Landau equation. In the limiting case, when the modulus of ellipticity approaches unity, these solutions approach optical solitons. This paper lists the dark-singular combo optical solitons.

The soliton solutions are extracted from the Lakshmanan–Porsezian–Daniel model by the aid of modified simple equation method. There are three forms of fibers that are studied and they represent Kerr law, parabolic law and anti-cubic law. The implementation of the scheme yields dark and singular soliton solutions to the model. The constraint conditi...

The dynamics of soliton propagation through optical fibers, modeled by perturbed Kundu–Eckhaus equation, is studied in this paper by the aid of extended trial function scheme. The perturbation terms are all of Hamiltonian type that appears with full nonlinearity. Bright and singular soliton solutions are secured with this integration scheme.

This paper studies soliton perturbation in optical metamaterials, with anti-cubic nonlinearity, by implementing three integration schemes. Bright, dark and singular soliton solutions are retrieved. The existence criteria of these solitons in metamaterials are also presented.

This paper addresses the dynamics of optical solitons in the presence of perturbation terms by the aid of three integration schemes. They are modified simple equation method, trial equation scheme, and the extended trial equation scheme. There are three types of nonlinearities that are studied in this paper which are Kerr law, power law, and logari...

This paper retrieves dispersive optical soliton solutions to Schrödinger-Hirota equation in birefringent fibesr that models dispersive optical soliton propagation. The extended trial equation method is the integration algorithm employed here. Bright and singular solitons solutions are obtained along with other forms of solutions such as snoidal wav...

Optical solitons in birefringent fibers with the effect of four-wave mixing having both parabolic and Kerr law nonlinearity are obtained by the modified simple equation scheme and the trial equation approach. Dark, bright as well as singular soliton type solutions are derived. Also, the two integration schemes give rise to additional solutions such...

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.

This paper retrieves bright and singular dispersive optical soliton solutions in optical fibers. The governing model is Schrödinger–Hirota equation. The existence criteria for these solitons are also enumerated.

The soliton dynamics in optical fibers with Fokas–Lenells equation is illustrated in this paper. Bright, dark and singular soliton solutions are retrieved along with few forms of combo–soliton solutions that also naturally emerged from the three integration schmes applied to the model. The existence criteria of these solitons are also presented.

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 solu...

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 s...

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.

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 solut...

This paper obtained singular and dark-singular combo solitons to Fokas–Lenells equation by the aid of traveling wave hypothesis. The modified simple equation scheme retrieved plane wave solutions to the model. The existence criteria of these waves are also presented.

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.