scholarly journals Numerical Approximation of The Weakly Damped Nonlinear Schrödinger Equation

2001 ◽  
Vol 1 (4) ◽  
pp. 319-332 ◽  
Author(s):  
Raimondas Čiegis ◽  
Violeta Pakenienė
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Optical Fibers ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Stability And Convergence ◽  
Nonlinear Schrödinger ◽  
The Stability ◽  
Nicolson Scheme ◽  
Crank Nicolson

AbstractIn this paper we consider the one-dimensional nonlinear Schrödinger equation. The equation includes an absorption term, and the solution is periodically amplified in order to compensate the lose of the energy. The problem describes propa- gation of a signal in optical fibers. In our previous work we proved that the well-known Crank—Nicolson scheme is unconditionally unstable for this problem. We present in this paper two finite difference approximations. The first one is given by a modified Crank—Nicolson scheme and the second one is obtained by a splitting scheme. The stability and convergence of these schemes are proved. The results of numerical exper- iments are presented and discussed.

scholarly journals Obtaining Optical Solitons via Resonant Nonlinear Schröndinger’s Equation for Optical Fiber Application

2021 ◽  
Author(s):  
Ali Tozar ◽  
Orkun Tasbozan ◽  
Ali Kurt
Keyword(s):  
Nonlinear Optics ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Optical Fibers ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Wave Form ◽  
Important Place ◽  
Nonlinear Schrödinger

Abstract Solitons which can be described as a localized wave form that maintain their shape after a collision with another soliton have became a very important phenomena in nonlinear optics due to their potential. They can be used as lossless information carriers in optical fibers due to their robustness arising from their particle grade stability upon a collision. Many scientists from various areas including electronic communication engineers have made solitons the main subject of study. Analytical solutions of nonlinear Schrödinger equation have a very important place in these studies. With the progress of nonlinear optics, some types of nonlinear Schrödinger equation have been derived for better understanding. Resonant nonlinear Schrödinger equation which is being used for describing nonlinear optical phenomena is a generic example for newly derived nonlinear Schrödinger equation. In this study, resonant nonlinear Schrödinger equation has been solved by using functional variable method and sixteen new soliton solutions have been obtained

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