scholarly journals Novel Optical Solitons to the Perturbed Gerdjikov-Ivanov Equation Via Collective Variables

2021 ◽  
Author(s):  
Zara Hassan ◽  
Nauman Raza ◽  
Francisco Gomez
Keyword(s):  
Optical Fibers ◽  
Soliton Solutions ◽  
Coupled System ◽  
Propagation Distance ◽  
Collective Variable ◽  
Temporal Position ◽  
Collective Variables ◽  
Pulse Parameters ◽  
Runge Kutta Method ◽  
Important Form

Abstract The objective of this research is to study the collective variable (CV) technique to explore an important form of Schrödinger equation known as the Gerdjikov-Ivanov (GI) equation which expresses the dynamics of solitons for optical fibers in terms of pulse parameters. These parameters are temporal position, amplitude, width, chirp, phase, and frequency known as collective variables (CVs). This is an effective and dynamic mathematical gadget to obtain soliton solutions of non-dimensional as well as perturbed GI equations. Moreover, an established numerical scheme that is the fourth-order Runge-Kutta method is exerted for the numerical simulation of the revealing coupled system of six ordinary differential equations which represent all the CVs included in the pulse ansatz. The CV approach is used to determine the evolution of pulse parameters with the propagation distance and illustrated it illustrated it graphically. Furthermore, Figures show the compelling periodic oscillations of pulse chirp, width, frequency and amplitude of soliton. For various values of super-Gaussian pulse parameters, the numerical behavior of solitons to illustrate variations in CVs is provided. Other significant aspects with regards to the current investigation are also inferred.

Optical solitons for the Kaup–Newell equation by collective variables method

2021 ◽  
Author(s):  
A. A. Al Qarni ◽  
A. A. Alshaery ◽  
H. O. Bakodah
Keyword(s):  
Short Pulse ◽  
Center Of Mass ◽  
Collective Variable ◽  
Temporal Position ◽  
Solitary Wave Solutions ◽  
Collective Variables ◽  
Nonlinear Parameters ◽  
Ultra Short Pulse ◽  
Parameter Values ◽  
Frequency Phase

In this work, we present a collective variable (CV) approach to establish dispersive solitary wave solutions for the Kaup–Newell Equation (KNE). The full CV theory has been utilized to enunciate the soliton molecules through its ground-laying parameters including the power of each pulse, phase and center-of-mass. Additionally, the dynamics of an ultra short pulse has been analyzed by using CV. This work may be utilized for various dynamics of solitons as well as the influence the amplitude, temporal position, frequency, phase and chirp on the solitons’ nonlinear parameters. Moreover, the numerical simulations have been designed by means of appropriate parameter values to explain more on the obtained results.

Tunnelling Effects of Solitons in Optical Fibers with Higher-Order Effects

2012 ◽  
Vol 67 (6-7) ◽  
pp. 338-346
Author(s):  
Chao-Qing Dai ◽  
Hai-Ping Zhu ◽  
Chun-Long Zheng
Keyword(s):  
Optical Fibers ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Higher Order ◽  
Order Effects ◽  
Bright Solitons ◽  
Dark Solitons ◽  
Tunnelling Effect ◽  
Tunnelling Effects ◽  
Higher Order Effects

We construct four types of analytical soliton solutions for the higher-order nonlinear Schrödinger equation with distributed coefficients. These solutions include bright solitons, dark solitons, combined solitons, and M-shaped solitons. Moreover, the explicit functions which describe the evolution of the width, peak, and phase are discussed exactly.We finally discuss the nonlinear soliton tunnelling effect for four types of femtosecond solitons

Dynamics of optical solitons incorporating Kerr dispersion and self-frequency shift

2019 ◽  
Vol 33 (19) ◽  
pp. 1950220
Author(s):  
Asma Rashid Butt ◽  
Muhammad Abdullah ◽  
Nauman Raza
Keyword(s):  
Frequency Shift ◽  
Optical Fibers ◽  
Laser Light ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Optical Solitons ◽  
Light Pulses ◽  
Ode Method ◽  
Analytical Approaches ◽  
Extended Trial

This paper deals with the dynamics of optical solitons in nonlinear Schrödinger equation (NLSE) with cubic-quintic law nonlinearity in the presence of self-frequency shift and self-steepening. This type of equation describes the ultralarge capacity transmission and traveling of laser light pulses in optical fibers. Two robust analytical approaches are employed to determine contemporary solutions. Some new explicit rational, periodic and combo periodic soliton solutions are extracted using the extended trial equation method. The Riccati–Bernoulli sub-ODE method provided us with singular and dark soliton solutions. The constraints found are necessary for the existence of solitons.

A novel type of soliton solutions for the Fokas–Lenells equation arising in the application of optical fibers

2020 ◽  
pp. 2150058
Author(s):  
Yasir Khan
Keyword(s):  
Variational Principle ◽  
Physical Function ◽  
Optical Fibers ◽  
Soliton Solutions ◽  
Fractal Model ◽  
Innovative Research ◽  
Theory Of Variation ◽  
Research Frontiers

The Fokas–Lenells (FL) equation is analyzed in this paper as an ironic physical function in optical fibers. A class of FL-equation soliton solutions is constructed by He’s variational principle. Besides, the fractal model of FL and its theory of variation are established. This paper focuses on the innovative research frontiers of FL equation.

Construction of optical soliton solutions of the generalized nonlinear Radhakrishnan–Kundu–Lakshmanan dynamical equation with power law nonlinearity

2020 ◽  
Vol 34 (13) ◽  
pp. 2050139 ◽  
Author(s):  
Aly R. Seadawy ◽  
Sultan Z. Alamri ◽  
Haya M. Al-Sharari
Keyword(s):  
Optical Fibers ◽  
Dynamical Equation ◽  
Physical Phenomenon ◽  
Soliton Solutions ◽  
Optical Soliton ◽  
Solitary Wave Solutions ◽  
Light Pulses ◽  
Wave Solutions ◽  
Different Types ◽  
Modified Simple Equation Method

The propagation of soliton through optical fibers has been studied by using nonlinear Schrödinger’s equation (NLSE). There are different types of NLSEs that study this physical phenomenon such as (GRKLE) generalized Radhakrishnan–Kundu–Lakshmanan equation. The generalized nonlinear RKL dynamical equation, which presents description of the dynamical of light pulses, has been studied. We used two formulas of the modified simple equation method to construct the optical soliton solutions of this model. The obtained solutions can be represented as bistable bright, dark, periodic solitary wave solutions.

scholarly journals Magnetooptics in Cylindrical Structures

2018 ◽  
Vol 8 (12) ◽  
pp. 2547 ◽  
Author(s):  
Štefan Višňovský
Keyword(s):  
Refractive Index ◽  
Optical Fibers ◽  
Yttrium Iron Garnet ◽  
Propagation Distance ◽  
Refractive Index Profile ◽  
Cylindrical Symmetry ◽  
Yttrium Iron ◽  
Helmholtz Equations ◽  
Cylindrical Structures ◽  
Iron Garnet

Understanding magnetooptics in cylindrical structures presents interest in the development of magnetic sensor and nonreciprocal devices compatible with optical fibers. The present work studies wave propagation in dielectric circular cylindrical structures characterized by magnetic permeability and electric permittivity tensors at axial magnetization. The Helmholtz equations deduced from the Maxwell equations in transverse circularly polarized representation provide electric and magnetic fields. With the restriction to terms linear in off-diagonal tensor elements, these can be expressed analytically. The results are applied to magnetooptic (MO) circular cylindrical waveguides with a step refractive index profile. The nonreciprocal propagation is illustrated on waveguides with an yttrium iron garnet (YIG) core and a lower refractive index cladding formed by gallium substituted yttrium iron garnet (GaYIG) at the optical communication wavelength. The propagation distance required for the isolator operation is about one hundred micrometers. The approach may be applied to other structures of cylindrical symmetry in the range from microwave to optical frequencies.

Optical soliton solutions for nonlinear complex Ginzburg–Landau dynamical equation with laws of nonlinearity Kerr law media

2020 ◽  
Vol 34 (19) ◽  
pp. 2050179
Author(s):  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Fiber Optics ◽  
Optical Fibers ◽  
Landau Equation ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Power Laws ◽  
Optical Soliton ◽  
Quantum Plasma ◽  
Ginzburg Landau ◽  
Soliton Dynamics

In this research article, our aim is to construct new optical soliton solutions for nonlinear complex Ginzburg–Landau equation with the help of modified mathematical technique. In this work, we studied both laws of nonlinearity (Kerr and power laws). The obtained solutions represent dark and bright solitons, singular and combined bright-dark solitons, traveling wave, and periodic solitary wave. The determined solutions provide help in the development of optical fibers, soliton dynamics, and nonlinear optics. The constructed solitonic solutions prove that the applicable technique is more reliable, efficient, fruitful and powerful to investigate higher order complex nonlinear partial differential equations (PDEs) involved in mathematical physics, quantum plasma, geophysics, mechanics, fiber optics, field of engineering, and many other kinds of applied sciences.

INTEGRABLE ASPECTS AND SOLITON-LIKE SOLUTIONS OF AN INHOMOGENEOUS COUPLED HIROTA–MAXWELL–BLOCH SYSTEM IN OPTICAL FIBERS WITH SYMBOLIC COMPUTATION

2010 ◽  
Vol 25 (16) ◽  
pp. 1365-1381 ◽  
Author(s):  
YU-SHAN XUE ◽  
BO TIAN ◽  
HAI-QIANG ZHANG ◽  
LI-LI LI
Keyword(s):  
Symbolic Computation ◽  
Optical Fibers ◽  
Soliton Solutions ◽  
Graphical Analysis ◽  
Envelope Soliton ◽  
Fiber Communication ◽  
Erbium Doped ◽  
Higher Order Dispersion ◽  
Interaction Behaviors ◽  
Soliton Excitation

For describing wave propagation in an inhomogeneous erbium-doped nonlinear fiber with higher-order dispersion and self-steepening, an inhomogeneous coupled Hirota–Maxwell–Bloch system is considered with the aid of symbolic computation. Through Painlevé singularity structure analysis, the integrable condition of such a system is analyzed. Via the Painlevé-integrable condition, the Lax pair is explicitly constructed based on the Ablowitz–Kaup–Newell–Segur scheme. Furthermore, the analytic soliton-like solutions are obtained via the Darboux transformation which makes it exercisable to generate the multi-soliton solutions in a recursive manner. Through the graphical analysis of some obtained analytic one- and two-soliton-like solutions, our concerns are mainly on the envelope soliton excitation, the propagation features of optical solitons and their interaction behaviors in actual fiber communication. Finally, the conservation laws for the system are also presented.

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