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Your search keyword '"Khan, Salam"' showing total 253 results
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253 results on '"Khan, Salam"'

25. Chirped gap solitons in fiber Bragg gratings with polynomial law of nonlinear refractive index

Author

Al-Ghafri Khalil S., Sankar Mani, Krishnan Edamana V., Khan Salam, and Biswas Anjan

Subjects
chirped solitons, bragg gratings, polynomial law, Applied optics. Photonics, TA1501-1820, Optics. Light, QC350-467
Abstract

The objective of the present study is to examine the behaviors of chirped optical solitons in fiber Bragg gratings (BGs) with dispersive reflectivity. The form of nonlinear refractive index represents polynomial law nonlinearity. By virtue of phase-matching condition, the discussed model of coupled nonlinear Schrödinger equation is reduced to an integrable form. Consequently, chirped optical solitons having various profiles such as W-shaped, bright, dark, kink and anti-kink solitons are derived. Further to this, the chirp associated with these soliton structures are extracted. The impact of dispersive reflectivity, self-phase modulation and cross-phase modulation on the pulse propagation is investigated and it is induced that the changes of self-phase modulation and cross-phase modulation cause a marked rise in soliton amplitude which is subject to minor variations by dispersive reflectivity. The physical evolutions of chirped optical solitons are described along with the corresponding chirp to pave the way for possible applications in the field of fiber BGs.

Published
2023
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42. On the eventual periodicity of fractional order dispersive wave equations using RBFS and transform

Author

Jan, Hameed Ullah, Uddin, Marjan, Shah, Irshad Ali, and Khan, Salam Ullah

Subjects
Laplace Transform, Time-Fractional KdV and Burgers Equations, General Engineering, General Physics and Astronomy, RBFs Methods, RBF-FD Method
Abstract

In this research work, let’s focus on the construction of numerical scheme based on radial basis functions finite difference (RBF-FD) method combined with the Laplace transform for the solution of fractional order dispersive wave equations. The numerical scheme is then applied to examine the eventual periodicity of the proposed model subject to the periodic boundary conditions. The implementation of proposed technique for high order fractional and integer type nonlinear partial differential equations (PDEs) is beneficial because this method is local in nature, therefore it yields and resulted in sparse differentiation matrices instead of full and dense matrices. Only small dimensions of linear systems of equations are to be solved for every center in the domain and hence this procedure is more reliable and efficient to solve large scale physical and engineering problems in complex domain. Laplace transform is utilized for obtaining the equivalent time-independent equation in Laplace space and also valuable to handle time-fractional derivatives in the Caputo sense. Application of Laplace transform avoids the time steeping procedure which commonly encounters the time instability issues. The solution to the transformed model is then obtained by computing the inversion of Laplace transform with an appropriate contour in a complex space, which is approximated by trapezoidal rule with high accuracy. Also since the Laplace transform operator is linear, it cannot be used to transform non-linear terms therefore let’s use a linearization approach and an appropriate iterative scheme. The proposed approach is tasted for some nonlinear fractional order KdV and Burgers equations. The capacity, high order accuracy and efficiency of our approach are demonstrated using examples and resultsRBFs Methods

Published
2022

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