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.

SPATIAL XPM-PAIRED SOLITONS IN NONLINEAR METAMATERIALS

2013 ◽  
Vol 22 (01) ◽  
pp. 1350009
Author(s):  
ANLE FANG ◽  
YUANJIANG XIANG ◽  
BINXIAN ZHUANG ◽  
LEYONG JIANG ◽  
XIAOYU DAI ◽  
...  
Keyword(s):  
Refractive Index ◽  
Optical Fibers ◽  
Function Method ◽  
Hyperbolic Function ◽  
Nonlinear Polarization ◽  
Dark Solitons ◽  
Nonlinear Metamaterials ◽  
Theoretical Predictions ◽  
Hyperbolic Function Method ◽  
Propagation Properties

We investigate spatial XPM-paired solitons in nonlinear metamaterials (MMs) based on the (1 + 1)-dimensional coupled nonlinear Schrodinger equation (NLSE) describing the co-propagation of two optical beams of different frequencies in the MM with a Kerr-type nonlinear polarization. Three types of XPM-paired solitons including bright-bright, bright-dark and dark-dark solitons for different combination of the signs of refractive index experienced by the two beams, respectively, are obtained by using a generalized hyperbolic function method, which makes the temporal XPM-paired solitons in optical fibers find their spatial counterparts in MMs. Numerical simulations are performed to confirm the theoretical predictions and further identify the propagation properties of the spatial XPM-paired solitons in MMs described by Drude model.

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.

scholarly journals On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Coatings ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1429
Author(s):  
Muhammad Imran Asjad ◽  
Hamood Ur Rehman ◽  
Zunaira Ishfaq ◽  
Jan Awrejcewicz ◽  
Ali Akgül ◽  
...  
Keyword(s):  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Hyperbolic Function ◽  
Nonlinear Phenomena ◽  
3D Graphics ◽  
New Exact Solutions ◽  
Hyperbolic Function Method ◽  
The Common ◽  
2D And 3D ◽  
Exact Soliton Solutions

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

New optical soliton solutions via two distinctive schemes for the DNA Peyrard–Bishop equation in fractal order

2021 ◽  
pp. 2150444
Author(s):  
Loubna Ouahid ◽  
M. A. Abdou ◽  
S. Owyed ◽  
Sachin Kumar
Keyword(s):  
Evolution Equations ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Optical Soliton ◽  
Nonlinear Evolution Equations ◽  
Hyperbolic Function ◽  
Closed Form Solutions ◽  
Special Solutions ◽  
Engineering Physics ◽  
Exact Soliton Solutions

The deoxyribonucleic acid (DNA) dynamical equation, which emerges from the oscillator chain known as the Peyrard–Bishop (PB) model for abundant optical soliton solutions, is presented, along with a novel fractional derivative operator. The Kudryashov expansion method and the extended hyperbolic function (HF) method are used to construct novel abundant exact soliton solutions, including light, dark, and other special solutions that can be directly evaluated. These newly formed soliton solutions acquired here lead one to ask whether the analytical approach could be extended to deal with other nonlinear evolution equations with fractional space–time derivatives arising in engineering physics and nonlinear sciences. It is noted that the newly proposed methods’ performance is most reliable and efficient, and they will be used to construct new generalized expressions of exact closed-form solutions for any other NPDEs of fractional order.

A modified hyperbolic function method and its application to the Toda lattice

2006 ◽  
Vol 172 (2) ◽  
pp. 938-945 ◽  
Author(s):  
Hongyan Zhi ◽  
Xueqin Zhao ◽  
Zhongyuan Yang ◽  
Hongqing Zhang
Keyword(s):  
Function Method ◽  
Toda Lattice ◽  
Hyperbolic Function ◽  
Hyperbolic Function Method

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 Improved hyperbolic function method and exact solutions for variable coefficient Benjamin-Bona-Mahony-Burgers equation

2015 ◽  
Vol 19 (4) ◽  
pp. 1183-1187
Author(s):  
Hong-Cai Ma ◽  
Xiao-Fang Peng ◽  
Dan-Dan Yao
Keyword(s):  
Fluid Mechanics ◽  
Exact Solutions ◽  
Variable Coefficient ◽  
Function Method ◽  
Burgers Equation ◽  
Periodic Wave ◽  
Hyperbolic Function ◽  
Hyperbolic Function Method

By using the improved hyperbolic function method, we investigate the variable coefficient Benjamin-Bona-Mahony-Burgers equation which is very important in fluid mechanics. Some exact solutions are obtained. Under some conditions, the periodic wave leads to the kink-like wave.

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.

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