Modulation instability analysis of the generalized nonlinear Schrödinger equation and its bright, dark and complexiton soliton solutions

Optik ◽  
2019 ◽  
Vol 183 ◽  
pp. 381-388 ◽  
Author(s):  
Jin-Jin Mao ◽  
Shou-Fu Tian ◽  
Tian-Tian Zhang ◽  
Xing-Jie Yan
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Nonlinear Schrodinger Equation ◽  
Instability Analysis ◽  
Nonlinear Schrödinger ◽  
Generalized Nonlinear Schrödinger Equation

scholarly journals Optical solitons and modulation instability analysis to the quadratic-cubic nonlinear Schrödinger equation

2018 ◽  
Vol 24 (1) ◽  
pp. 20-33 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Integration Scheme ◽  
Instability Analysis ◽  
Nonlinear Schrödinger

This paper obtains the dark, bright, dark-bright, dark-singular optical and singular soliton solutions to the nonlinear Schrödinger equation with quadratic-cubic nonlinearity (QC-NLSE), which describes the propagation of solitons through optical fibers. The adopted integration scheme is the sine-Gordon expansion method (SGEM). Further more, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis, and the MI gain spectrum is got. Physical interpretations of the acquired results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the PNSE.

The M-fractional improved perturbed nonlinear Schrödinger equation: Optical solitons and modulation instability analysis

2021 ◽  
pp. 2150121
Author(s):  
Eied M. Khalil ◽  
T. A. Sulaiman ◽  
Abdullahi Yusuf ◽  
Mustafa Inc
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Modulation Instability ◽  
Nonlinear Schrodinger Equation ◽  
Instability Analysis ◽  
Nonlinear Schrödinger ◽  
The Stability ◽  
The Waves

In order to obtain some novel analytical solutions for fractional improved nonlinear Schrodinger equation with perturbation, the polynomial expansion, simplest equation and extended sine-Gordon expansion schemes are utilized. A collection of different types of solitons are reported with a physical and important perspective, containing optical dark solitons. The methods reveal the solutions in a structure of rapidly converging series. This research highlights additional important features of the methods being considered. In addition, the modulation instability analysis is carried out to discuss the stability analysis of the solutions reached, and the movement role of the waves is examined, which affirms that all the established solutions are exact and stable.

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