Dynamics of optical pulses in fiber optics

2021 ◽  
Author(s):  
U. Younas ◽  
J. Ren ◽  
M. Bilal
Keyword(s):  
Fiber Optics ◽  
Diffusion Processes ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Short Pulses ◽  
Nonlinear Dynamical ◽  
Solution Structures ◽  
Integration Techniques ◽  
Complex Phenomena

In this paper, we pay attention to the nonlinear dynamical behavior of ultra-short pulses in optical fiber. The new Hamiltonian amplitude equation is used as a governing model to analyze the pulses. We secure the ultra-short pulses in the forms of bright, dark, singular, combo and complex soliton solutions by the utilization of three of sound computational integration techniques that are protracted (or extended) Fan-sub equation method (PFSEM), the generalized exponential rational function method (GERFM), extended Sinh-Gordon equation expansion method (ShGEEM). Moreover, Jacobi’s elliptic, trigonometric, and hyperbolic functions solutions are also discussed as well as the constraint conditions of the achieved solutions are also presented. In addition, we discuss the different wave structures by the assistance of logarithmic transformation. The findings demonstrate that the examined equation theoretically contains a large number of soliton solution structures. By selecting appropriate criteria, the actual portrayal of certain obtained results is sorted out graphically in 3D and 2D profiles. The results suggest that the procedures used are concise, direct, and efficient, and that they can be applied to more complex phenomena. The resulting solutions are novel, intriguing, and potentially useful in understanding energy transit and diffusion processes in mathematical models of several disciplines of interest, including nonlinear optics. Our new results have been compared to these in the literature.

Solitons and other solutions of the long-short wave equation

2015 ◽  
Vol 25 (1) ◽  
pp. 129-145 ◽  
Author(s):  
Ghodrat Ebadi ◽  
Aida Mojaver ◽  
Sachin Kumar ◽  
Anjan Biswas
Keyword(s):  
Wave Equation ◽  
Water Waves ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Short Wave ◽  
Shallow Water Waves ◽  
Content Type ◽  
Integration Techniques ◽  
Physical Phenomena ◽  
The Waves

Purpose – The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others. Design/methodology/approach – The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results. Findings – The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions. Originality/value – The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

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.

New exact solitary waves solutions to the fractional Fokas-Lenells equation via Atangana-Baleanu derivative operator

2020 ◽  
Vol 34 (31) ◽  
pp. 2050309
Author(s):  
Hadi Rezazadeh ◽  
Abbagari Souleymanou ◽  
Alper Korkmaz ◽  
Mostafa M. A. Khater ◽  
Serge P. T. Mukam ◽  
...  
Keyword(s):  
Optical Fibers ◽  
Solitary Waves ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Short Wave ◽  
Derivative Operator ◽  
Short Pulses

In this research, a particular attention has been given on the fractional Fokas-Lenells equation via Atangana-Baleanu derivative operator that describe the propagation of short pulses in optical fibers. The integrability properties has been investigated while using the modified Khater method that we present in details. As a result, number of new soliton solutions are obtained along with constraints on some parameters that are introduced accordingly. For further details about our obtained solutions, some distinct types of solutions have been illustrated to explain more physical and dynamical behavior of the short wave pulses in the optical fibers.

Dynamical structures of solitons and some new types of exact solutions for the (2+1)-dimensional DJKM equation using Lie symmetry analysis

2020 ◽  
pp. 2150015
Author(s):  
Sachin Kumar ◽  
Amit Kumar
Keyword(s):  
Exact Solutions ◽  
Fiber Optics ◽  
Statistical Physics ◽  
Vector Fields ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Lie Symmetry ◽  
Group Theoretic Method ◽  
Kink Wave ◽  
Djkm Equation

This paper is devoted to obtaining some new types of exact solutions of the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation utilizing the Lie symmetry method. All the Lie symmetries, infinitesimal generators, and possible geometric vector fields have been obtained by using the invariance condition of the group-theoretic method. Meanwhile, the Lie symmetry reductions and explicit exact solutions are obtained by a one-dimensional (1D) optimal system. All the obtained exact solutions are absolutely new and completely different from the earlier established results in the literature. Moreover, the dynamical behavior of obtained solitons like doubly solitons, dark solitons, kink wave, curved shaped multi-solitons, parabolic waves, solitary waves, and annihilation of elastic multi-soliton profiles is depicted graphically via interesting 3D-shapes. That will be widely used to provide many more attractive complex physical phenomena in the fields of plasma physics, statistical physics, fiber optics, fluid dynamics, condensed matter physics, and so on. Finally, we have verified all the achieved soliton solutions through symbolic computations with Mathematica.

scholarly journals Bistable dynamics beyond rotating wave approximation

2014 ◽  
Vol 23 (02) ◽  
pp. 1450019 ◽  
Author(s):  
Y. A. Sharaby ◽  
S. Lynch ◽  
A. Joshi ◽  
S. S. Hassan
Keyword(s):  
Ring Cavity ◽  
Dynamical Behavior ◽  
Single Mode ◽  
Unstable State ◽  
Nonlinear Dynamical ◽  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Atomic Medium ◽  
Bistable Dynamics ◽  
Rotating Wave

In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.

New Exact Solutions for Two Nonlinear Equations

2006 ◽  
Vol 61 (1-2) ◽  
pp. 1-6 ◽  
Author(s):  
Zonghang Yang
Keyword(s):  
Wave Equation ◽  
Partial Differential Equations ◽  
Exact Solutions ◽  
Water Wave ◽  
Function Method ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
New Exact Solutions ◽  
Complex Phenomena ◽  
Sivashinsky Equation

Nonlinear partial differential equations are widely used to describe complex phenomena in various fields of science, for example the Korteweg-de Vries-Kuramoto-Sivashinsky equation (KdV-KS equation) and the Ablowitz-Kaup-Newell-Segur shallow water wave equation (AKNS-SWW equation). To our knowledge the exact solutions for the first equation were still not obtained and the obtained exact solutions for the second were just N-soliton solutions. In this paper we present kinds of new exact solutions by using the extended tanh-function method.

An explicit plethora of soliton solutions for a new microtubules transmission lines model: A fractional comparison

2021 ◽  
Author(s):  
Nauman Raza ◽  
Ziyad A. Alhussain
Keyword(s):  
Nonlinear Dynamics ◽  
Transmission Lines ◽  
Fractional Derivatives ◽  
Intracellular Transport ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Algebraic Method ◽  
Governing System ◽  
Parameter Values ◽  
Fractional Parameter

This paper introduces a new fractional electrical microtubules transmission lines model in the sense of Atangana–Baleanu and beta derivatives to comprehend nonlinear dynamics of the governing system. This structure possesses one of the most important parts in cellular process biology and fractional parameter incorporates the memory effects in microtubules. Also, microtubules are extremely beneficial in cell motility, signaling and intracellular transport. The new extended direct algebraic method is a compelling and persuasive integrating scheme to extract soliton solutions. The retrieved solutions include dark, bright and singular solitons. This model executes a prominent part in exhibiting the wave transmission in nonlinear systems. The novelty and advantage of the proposed method are portrayed by applying it to this model and its dynamical behavior is depicted by 3D and 2D plots. A comparative study of two fractional derivatives at distinct fractional parameter values and graphics of sensitivity analysis is also carried out in this paper.

Dynamical Variation of Weierstrass-Mandelbrot Function in Higher Dimensional Space

2013 ◽  
Vol 470 ◽  
pp. 767-771
Author(s):  
L. Zhang ◽  
Shu Tang Liu
Keyword(s):  
Hurst Exponent ◽  
Dimensional Space ◽  
Dynamical Behavior ◽  
Fractal Dimensions ◽  
Statistical Characteristics ◽  
3 Dimensional ◽  
Higher Dimensional ◽  
Complex Phenomena ◽  
Real Complex

Many real complex phenomena are related with Weierstrass-Mandelbrot function (WMF). Most researches focus on the systems as parameters fixed, such as calculations of its different fractal dimensions or the statistical characteristics of its generalized form and so on. Moreover, real systems always change according to different environments, so that to study the dynamical behavior of these systems as parameters change is important. However, there is few results about this aim. In this paper, we propose simulated results for the effects of parameters changeably on the graph of WMF in higher dimensional space. In addition, the relationships between the Hurst exponent of WMF and its parameters dynamically in 2-and 3-dimensional spaces are also given.

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