Benchmarking of the Split-Step Fourier Method on Solving a Soliton Propagation Equation in a Nonlinear Optical Medium

2020 ◽  
Vol 12 (2) ◽  
pp. 105-112
Author(s):  
Ahmad Ripai ◽  
Zulfi Abdullah ◽  
Mahdhivan Syafwan ◽  
Wahyu Hidayat
Keyword(s):  
Optical Fiber ◽  
Nonlinear Optical ◽  
Fourier Method ◽  
Optical Solitons ◽  
Propagation Equation ◽  
Dispersion Parameters ◽  
Nls Equation ◽  
Soliton Propagation ◽  
Optical Medium ◽  
Nonlinear Schrödinger

Benchmarking of the numerical split-step Fourier method in solving a soliton propagation equation in a nonlinear optical medium is considered. This study is carried out by comparing the solutions calculated by numerics with those obtained by analytics. In particular, the soliton propagation equation used as the object of observation is the nonlinear Schrödinger (NLS) equation, which describes optical solitons in optical fiber. By using the split-step Fourier method, we show that the split-step Fourier method is accurate. We also confirm that the nonlinear and dispersion parameters of the optical fiber influence the soliton propagation.

Optical solitons and stability analysis for the generalized fourth-order nonlinear Schrödinger equation

2019 ◽  
Vol 33 (27) ◽  
pp. 1950333
Author(s):  
Xiao-Song Tang ◽  
Biao Li
Keyword(s):  
Nonlinear Dynamics ◽  
Fourth Order ◽  
Continuous Wave ◽  
Modulational Instability ◽  
Optical Solitons ◽  
Singular Solutions ◽  
Nls Equation ◽  
Ansatz Method ◽  
Nonlinear Schrödinger ◽  
Wave Solutions

We consider a generalized fourth-order nonlinear Schrödinger (NLS) equation. Based on the ansatz method, its bright, dark single-soliton is constructed under some constraint conditions. Furthermore, combining the Riccati equation extension approach, we also derive some exact singular solutions. With several parameters to play with, we display the dynamic behaviors of bright, dark single-soliton. Finally, the condition for the modulational instability (MI) of continuous wave solutions for the equation is generated. It is hoped that our results can help enrich the nonlinear dynamics of the NLS equations.

Modeling optical solitons in a practical lossy fiber

2000 ◽  
Vol 78 (12) ◽  
pp. 1087-1090
Author(s):  
M F Mahmood
Keyword(s):  
Optical Fiber ◽  
Variational Formulation ◽  
Analytical Investigation ◽  
Optical Solitons ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Optical Pulses ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

An analytical investigation is presented that is based on the Lagrangian variational formulation of the interaction of two orthogonally polarized optical pulses. The pulses are governed by a pair of coupled nonlinear Schrödinger equations in a practical lossy optical fiber. PACS Nos.: 03.40Kf, 42.65Tg, 42.81Dp

Stochastic Soliton Solutions of the High-Order Nonlinear Schrödinger Equation in the Optical Fiber with Stochastic Dispersion and Nonlinearity

2014 ◽  
Vol 69 (1-2) ◽  
pp. 21-33 ◽  
Author(s):  
Hui Zhong ◽  
Bo Tian
Keyword(s):  
Optical Fiber ◽  
White Noise ◽  
Gaussian White Noise ◽  
Soliton Solutions ◽  
Periodic Oscillation ◽  
Bound State ◽  
High Order ◽  
Soliton Propagation ◽  
Nonlinear Schrödinger ◽  
White Noise Functional

In this paper, the high-order nonlinear Schrödinger (HNLS) equation driven by the Gaussian white noise, which describes the wave propagation in the optical fiber with stochastic dispersion and nonlinearity, is studied. With the white noise functional approach and symbolic computation, stochastic one- and two-soliton solutions for the stochastic HNLS equation are obtained. For the stochastic one soliton, the energy and shape keep unchanged along the soliton propagation, but the velocity and phase shift change randomly because of the effects of Gaussian white noise. Ranges of the changes increase with the increase in the intensity of Gaussian white noise, and the direction of velocity is inverted along the soliton propagation. For the stochastic two solitons, the effects of Gaussian white noise on the interactions in the bound and unbound states are discussed: In the bound state, periodic oscillation of the two solitons is broken because of the existence of the Gaussian white noise, and the oscillation of stochastic two solitons forms randomly. In the unbound state, interaction of the stochastic two solitons happens twice because of the Gaussian white noise. With the increase in the intensity of Gaussian white noise, the region of the interaction enlarges.

Bright solitons and their interactions of the (3 + 1)-dimensional coupled nonlinear Schrödinger system for an optical fiber

2015 ◽  
Vol 29 (35n36) ◽  
pp. 1550245 ◽  
Author(s):  
Ya Sun ◽  
Bo Tian ◽  
Yu-Feng Wang ◽  
Yun-Po Wang ◽  
Zhi-Ruo Huang
Keyword(s):  
Optical Fiber ◽  
Soliton Solutions ◽  
Auxiliary Function ◽  
Bilinear Forms ◽  
Soliton Propagation ◽  
Nonlinear Schrödinger ◽  
Elastic Interactions ◽  
Bright Solitons ◽  
Nonlinear Schrödinger System ◽  
Schrödinger System

Under investigation in this paper is the [Formula: see text]-dimensional coupled nonlinear Schrödinger system for an optical fiber with birefringence. With the Hirota method, bilinear forms of the system are derived via an auxiliary function, and the bright one- and two-soliton solutions are constructed. Based on those soliton solutions, soliton propagation and interaction are investigated analytically and graphically. Non-singular cases of the bright one-soliton solutions are presented, from which the single-peak and two-peak solitons can arise, respectively. Through the analysis on the bright two-soliton solutions, the elastic and inelastic interactions are investigated. Three kinds of the elastic interactions are presented, between the two one-peak solitons, a one-peak soliton and a two-peak soliton, and the two two-peak solitons.

Optical solitons and stability analysis for the generalized second-order nonlinear Schrödinger equation in an optical fiber

2020 ◽  
Vol 21 (7-8) ◽  
pp. 855-863 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Ahmad Javid
Keyword(s):  
Stability Analysis ◽  
Schrödinger Equation ◽  
Optical Fiber ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Expansion Method ◽  
Optical Solitons ◽  
Nonlinear Schrodinger Equation ◽  
Second Order ◽  
Nonlinear Schrödinger

AbstractIn this paper, the generalized second-order nonlinear Schrödinger equation with light-wave promulgation in an optical fiber, is studied for optical soliton solutions. Three analytical methods such as the $\mathrm{exp}\left(-\phi \left(\chi \right)\right)$-expansion method, the G′/G2-expansion method and the first integral methods are used to extract dark, singular, periodic, dark-singular combo optical solitons for the proposed model. These solitons appear with constraint conditions on their parameters and they are also presented. These three strategic schemes have made this retrieval successful. The given model is also studied for modulation instability on the basis of linear stability analysis. A dispersion relation is obtained between wave number and frequency.

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