Fast Solution for the Nonlinear Schrodinger
Equation in Optical Fibers by the Reduced
Basis Method

Pa Mahmud Kah; Phineas Roy Kiogora; Kennedy Awuor; Churchill Saoke

doi:https://doi.org/10.14445/22315373/IJMTT-V68I1P512

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 1 | Year 2022 | Article Id. IJMTT-V68I1P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I1P512

Fast Solution for the Nonlinear Schrodinger Equation in Optical Fibers by the Reduced Basis Method

Pa Mahmud Kah, Phineas Roy Kiogora, Kennedy Awuor, Churchill Saoke

Citation :

Pa Mahmud Kah, Phineas Roy Kiogora, Kennedy Awuor, Churchill Saoke, "Fast Solution for the Nonlinear Schrodinger Equation in Optical Fibers by the Reduced Basis Method," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 1, pp. 101-114, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I1P512

Abstract

Nonlinear Schr¨odinger Equation (NLSE) is a universal nonlinear model which portrays several physical nonlinear systems. Among other natural phenomena the one-dimensional NLSE models, light pulses in optical fibers and the dilut-gas Bose-Einstein condensates (BEC) in quasi one-dimensional regime. In this research application of the NLSE in optical fibers is emphasized. However, the numerical solution for the NLSE encounters several computational challenges such as cost and time. Therefore, we employ the Reduced Basis Method (RBM) which significantly reduced these computational cost and time and thus accelerate numerical simulations. We came up with a faster and cheaper numerical solution of the NLSE in fiber optics and our results presented can be applied in communication systems.

Keywords

Dispersion, Fiber Optics, NLSE, Nonlinearity, RBM.

References

[1] A. A. Alanazi, S. Z. Alamri, S. Shafie, S. B. M. Puzi. Solving nonlinear schrodinger equation using stable implicit finite difference method in single-mode optical fibers. wileyonlinelibrary.com/journal/mma, (2021).
[2] Agrawal, G. Nonlinear fiber optics (fifth edition). Optics and Photonics, Academic Press, (2013)
[3] Agrawal, G. Nonlinear fiber optics (6th ed). New York: Academic Press, (2019)
[4] Ames, W. F. Nonlinear partial differential equations in engineering vol 18. (New York: Academic Press), (1965) 13
[5] Christian H. and Hendry D. P. Deep learning of the nonlinear schrodinger equation in fiber-optic communications. CoRR, (2018).
[6] Domenico F. A study of a nonlinear schrodinger equation for optical fibers. UNIVERSITA DEGLI STUDI DI FIRENZE, (2016).
[7] FEDERICO N. et al. Reduced basis method for parametrized elliptic optimal control problems. Society for Industrial and Applied Mathematics, 35 (5), A2316-A2340, (2013).
[8] Jeff H. Understanding fiber optics. LaserLight Press, (2006).
[9] Jens L. E. Reduced basis methods for parametrized partial differential equations. Norwegian University of Science and Technology, (2011).
[10] John C. Introduction to fiber optics. Newnes, (2001).
[11] Muhamad A. and Anak A. S. P. M. Analysis of high order dispersion and nonlinear effects in fiber optic transmission with nonlinear schrodinger equation model. International Conference on Quality in Research, (2015).
[12] P.Agrawal G. Nonlinear fiber optics 3rd edition. California, USA : Academic Press, (1995).
[13] P.Agrawal G. Fiber-optic communication systems. NY: John Wiley, Inc. USA, (2002).
[14] Rozza G. et al. Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic co- ercive partial differential equations: application to transport and continuum mechanics. Archives of Computational Methods in Engineering, 15(3):229275, (2008).
[15] Xu, Bo. Study of fiber nonlinear effects on fiber optic communnication system. A P.hD Dissertation, University of Virginia. (2003).