scholarly journals New Optical Solitons And Modulation Instability Analysis of Generalized Coupled Nonlinear Schrodinger-KdV System

2022 ◽  
Author(s):  
Thilagarajah Mathanaranjan
Keyword(s):  
Gordon Equation ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Optical Solitons ◽  
Ansatz Method ◽  
Instability Analysis ◽  
Nonlinear Schrödinger ◽  
Short Waves ◽  
Singular Soliton

Abstract In this study, the generalized coupled nonlinear Schrodinger-KdV (NLS-KdV) system is investigated to obtain new optical soliton solutions. This system appears as a model for reciprocity between long and short waves in various of physical settings. Different kind of new soliton solutions including dark, bright, combined dark-bright, singular and combined singular soliton solutions are obtained using two effective methods namely, the extended sinh-Gordon equation expansion method and the solitary wave ansatz method. In addition, the modulation instability analysis of the system is presented based on the standard linearstability analysis. The behaviours of obtained solutions are expressed by 3D graphs.

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.

scholarly journals Optical solitons to the fractional Schrödinger-Hirota equation

2019 ◽  
Vol 4 (2) ◽  
pp. 535-542 ◽  
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Hasan Bulut ◽  
Sibel Sehriban Atas
Keyword(s):  
Solitary Waves ◽  
Gordon Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Solitons ◽  
Hirota Equation ◽  
3 Dimensional ◽  
Peak Intensity ◽  
Singular Soliton

AbstractThis study reaches the dark, bright, mixed dark-bright, and singular optical solitons to the fractional Schrödinger-Hirota equation with a truncated M-fractional derivative via the extended sinh-Gordon equation expansion method. Dark soliton describes the solitary waves with lower intensity than the background, bright soliton describes the solitary waves whose peak intensity is larger than the background, and the singular soliton solutions is a solitary wave with discontinuous derivatives; examples of such solitary waves include compactions, which have finite (compact) support, and peakons, whose peaks have a discontinuous first derivative. The constraint conditions for the existence of valid solutions are given. We use some suitable values of the parameters in plotting 3-dimensional surfaces to some of the reported solutions.

Modulation instability analysis and optical solitons of the generalized model for description of propagation pulses in optical fiber with four non-linear terms

2020 ◽  
pp. 2150112
Author(s):  
S. U. Rehman ◽  
Aly R. Seadawy ◽  
M. Younis ◽  
S. T. R. Rizvi ◽  
T. A. Sulaiman ◽  
...  
Keyword(s):  
Optical Fibers ◽  
Modulation Instability ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Periodic Wave ◽  
Jacobi Elliptic Function ◽  
Arbitrary Power ◽  
Non Linear ◽  
Complex Phenomena ◽  
Singular Soliton

In this article, we investigate the optical soiltons and other solutions to Kudryashov’s equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as [Formula: see text]-model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations.

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