scholarly journals Exact Soliton Solutions for Nonlinear Perturbed Schrödinger Equations with Nonlinear Optical Media

2020 ◽  
Vol 10 (24) ◽  
pp. 8929
Author(s):  
Khaled A. Gepreel
Keyword(s):  
Optical Fibers ◽  
Power Law ◽  
Soliton Solutions ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Optical Media ◽  
Kerr Law ◽  
Exact Soliton Solutions

The nonlinear perturbed Schrödinger equations (NPSEs) with nonlinear terms as Kerr law, power law, quadratic-cubic law, and dual-power law nonlinearity media play an important role in optical fibers. In this article we implement the rational solitary wave method to study the NPSEs when nonlinear terms take some different forms. Additionally, we use the q-deformed hyperbolic function and q-deformed trigonometric function methods to study the exact solutions to NPSEs. Different kind of soliton solutions are obtained such as bright, dark, and singular periodic solutions to the NPSEs.

N-dark–dark solitons for the coupled higher-order nonlinear Schrödinger equations in optical fibers

2017 ◽  
Vol 31 (33) ◽  
pp. 1750305 ◽  
Author(s):  
Hai-Qiang Zhang ◽  
Yue Wang
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Dark Solitons ◽  
Nonlinear Schrodinger Equations

In this paper, we construct the binary Darboux transformation on the coupled higher-order dispersive nonlinear Schrödinger equations in optical fibers. We present the N-fold iterative transformation in terms of the determinants. By the limit technique, we derive the N-dark–dark soliton solutions from the non-vanishing background. Based on the obtained solutions, we find that the collision mechanisms of dark vector solitons exhibit the standard elastic collisions in both two components.

scholarly journals The conformable space–time fractional Fokas–Lenells equation and its optical soliton solutions based on three analytical schemes

2020 ◽  
pp. 2150004
Author(s):  
Asim Zafar ◽  
Muhammad Raheel ◽  
Ahmet Bekir ◽  
Waseem Razzaq
Keyword(s):  
Optical Fibers ◽  
Function Method ◽  
Pulse Propagation ◽  
Soliton Solutions ◽  
Space Time ◽  
Hyperbolic Function ◽  
Nonlinear Wave Propagation ◽  
Different Types ◽  
Hyperbolic Function Method ◽  
Exact Soliton Solutions

This paper is about the study of space–time fractional Fokas–Lenells equation that describes nonlinear wave propagation in optical fibers. Three prominent schemes are employed for extracting different types of exact soliton solutions. In particular, the [Formula: see text] function method, the hyperbolic function method and the simplest Riccati equation scheme are investigated for the said model. As a sequel, a series of soliton solutions are obtained and verified through MATHEMATICA. The obtained solutions are significant additions in some specific fields of physics and engineering. Furthermore, the 3D graphical descriptions are left to analyze the pulse propagation for the reader.

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