New Soliton Solutions of Optical Pulse Envelope E(Z, τ) with Beta Time Derivative

Optik ◽  
2020 ◽  
Vol 223 ◽  
pp. 165453
Author(s):  
Seyma Tuluce Demiray
Keyword(s):  
Optical Pulse ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Pulse Envelope

Dynamics of new optical solitons for the Triki–Biswas model using beta-time derivative

2021 ◽  
Author(s):  
Asim Zafar ◽  
Ahmet Bekir ◽  
M. Raheel ◽  
Kottakkaran Sooppy Nisar ◽  
Salman Mustafa
Keyword(s):  
Model Equation ◽  
Pulse Propagation ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Integration Schemes ◽  
Ultrashort Pulse Propagation ◽  
Different Types ◽  
Efficient Integration ◽  
Derivative Nonlinear Schrödinger Equation

This paper comprises the different types of optical soliton solutions of an important Triki–Biswas model equation with beta-time derivative. The beta derivative is considered as a generalized version of the classical derivative. The aforesaid model equation is the generalization of the derivative nonlinear Schrödinger equation that describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel beta derivative operator and three efficient integration schemes. During this work, a sequence of new optical solitons is produced that may have an importance in optical fiber systems. These solutions are verified and numerically simulated through soft computation.

SOLITON INTERACTIONS FOR A HIROTA–MAXWELL–BLOCH SYSTEM IN THE INHOMOGENEOUS ERBIUM-DOPED FIBER

2012 ◽  
Vol 26 (24) ◽  
pp. 1250115 ◽  
Author(s):  
M. WANG ◽  
B. TIAN ◽  
F.-H. QI ◽  
B. QIN ◽  
Z.-Q. LIN
Keyword(s):  
Optical Pulse ◽  
Modulational Instability ◽  
Soliton Solutions ◽  
Ultrashort Optical Pulse ◽  
Hirota Equation ◽  
Soliton Interactions ◽  
Erbium Doped ◽  
Induced Transparency ◽  
Higher Order Dispersion ◽  
Order Dispersion

In this paper, we consider a generalized Hirota–Maxwell–Bloch system with the higher-order dispersion and self-steepening effects, which describes the propagation of ultrashort optical pulse in the inhomogeneous erbium-doped fiber. Under certain coefficient constraints, N-soliton solutions are obtained through the Hirota method and symbolic computation. Soliton interactions are graphically presented and analyzed in the different fibers. Compared with the Hirota equation without the Maxwell–Bloch parts, the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. In addition, the amplitudes and widths of solitons are respectively observed to decrease and increase in the dispersion-decreasing and dispersion-increasing fibers. Finally, we give the modulational instability condition through the linear stability analysis.

scholarly journals Soliton Solutions for space-time fractional Heisenberg ferromagnetic spin chain equation by generalized Kudryashov method and modified exp -expansion function method

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 393
Author(s):  
S. Tuluce Demiray ◽  
U. Bayrakci
Keyword(s):  
Spin Chain ◽  
Function Method ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Bright Soliton ◽  
Integration Schemes ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Heisenberg Ferromagnetic Spin Chain ◽  
Chain Equation

This paper addresses the Heisenberg ferromagnetic spin chain equation with beta time derivative. Integration schemes are used to study this equation. They are generalized Kudryashov method and modified exp -expansion function method. Dark, bright and dark-bright soliton solutions of this equation are procured.

Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre

2016 ◽  
Vol 71 (1) ◽  
pp. 9-20 ◽  
Author(s):  
Zhe Gao ◽  
Yi-Tian Gao ◽  
Chuan-Qi Su ◽  
Qi-Min Wang ◽  
Bing-Qing Mao
Keyword(s):  
Conservation Laws ◽  
Darboux Transformation ◽  
Optical Pulse ◽  
Soliton Solutions ◽  
Rogue Waves ◽  
Pulse Frequency ◽  
Lax Pair ◽  
Tunneling Effect ◽  
Nonlinear Schrödinger ◽  
Erbium Doped

AbstractUnder investigation in this article is a generalised nonlinear Schrödinger-Maxwell-Bloch system for the picosecond optical pulse propagation in an inhomogeneous erbium-doped silica optical fibre. Lax pair, conservation laws, Darboux transformation, and generalised Darboux transformation for the system are constructed; with the one- and two-soliton solutions, the first- and second-order rogue waves given. Soliton propagation is discussed. Nonlinear tunneling effect on the solitons and rogue waves are investigated. We find that (i) the detuning of the atomic transition frequency from the optical pulse frequency affects the velocity of the pulse when the detuning is small, (ii) nonlinear tunneling effect does not affect the energy redistribution of the soliton interaction, (iii) dispersion barrier/well has an effect on the soliton velocity, whereas nonlinear well/barrier does not, (iv) nonlinear well/barrier could amplify/compress the solitons or rogue waves in a smoother manner than the dispersion barrier/well, and (v) dispersion barrier could “attract” the nearby rogue waves, whereas the dispersion well has a repulsive effect on them.

scholarly journals Different soliton solutions to the modified equal-width wave equation with Beta-time fractional derivative via two different methods

2021 ◽  
Vol 68 (1 Jan-Feb) ◽  
Author(s):  
Asim Zafar ◽  
Muhammad Raheel ◽  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Function Method ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Different Types ◽  
Non Linear ◽  
Time Fractional Derivative

‎In this paper‎, ‎different types of soliton solutions of the modified equal width wave (MEW) equation with beta time derivative are obtained by implementing the two different methods named as‎: ‎extended Jacobi's elliptic expansion function method and Kudryashov method‎. ‎The dark‎, ‎bright‎, ‎singular and other solitons are achieved‎. ‎The obtained soliton solutions are verified through MATHEMATICA‎. ‎At the end‎, ‎the results are also explained through graphs‎. ‎These soliton solutions suggest that these two methods are effective‎, ‎straight forward and reliable as compare to other methods‎. ‎The obtained results can be used in describing the substantial understanding of the studious structures as well as others related non-linear physical structures‎.

scholarly journals Numerical Wave Solutions for Nonlinear Coupled Equations using Sinc-Collocation Method

2015 ◽  
Vol 20 (2) ◽  
pp. 19 ◽  
Author(s):  
Kamel Al-Khaled
Keyword(s):  
Collocation Method ◽  
Numerical Solutions ◽  
Time Derivative ◽  
Soliton Solutions ◽  
Basis Functions ◽  
Coupled Equations ◽  
Kdv Equations ◽  
Difference Formula ◽  
Sinc Functions ◽  
Numerical Wave

In this paper, numerical solutions for nonlinear coupled Korteweg-de Vries(abbreviated as KdV) equations are calculated by the Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. The first step is to discretize time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.  

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