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

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2022 by IJMTT Journal
Volume-68 Issue-1
Year of Publication : 2022
Authors : Pa Mahmud Kah, Phineas Roy Kiogora, Kennedy Awuor, Churchill Saoke
  10.14445/22315373/IJMTT-V68I1P512

MLA

MLA Style: 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 68.1 (2022):101-114. 

APA Style: Pa Mahmud Kah, Phineas Roy Kiogora, Kennedy Awuor, Churchill Saoke(2022). Fast Solution for the Nonlinear Schrodinger Equation in Optical Fibers by the Reduced Basis Method. International Journal of Mathematics Trends and Technology, 68(1), 101-114.

Abstract
Nonlinear Schrodinger 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.

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Keywords : Dispersion, Fiber Optics, NLSE, Nonlinearity, RBM.