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.

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.

Refraction simulation of internal solitary waves for the fractional Benjamin–Ono equation in fluid dynamics

2021 ◽  
pp. 2150363
Author(s):  
Serbay Duran ◽  
Asıf Yokuş ◽  
Hülya Durur ◽  
Doğan Kaya
Keyword(s):  
Solitary Waves ◽  
Analytical Methods ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Stationary Wave ◽  
Dark Soliton ◽  
Internal Solitary Waves ◽  
Hyperbolic Complex ◽  
Singular Soliton

In this study, the modified [Formula: see text]-expansion method and modified sub-equation method have been successfully applied to the fractional Benjamin–Ono equation that models the internal solitary wave event in the ocean or atmosphere. With both analytical methods, dark soliton, singular soliton, mixed dark-singular soliton, trigonometric, rational, hyperbolic, complex hyperbolic, complex type traveling wave solutions have been produced. In these applications, we consider the conformable operator to which the chain rule is applied. Special values were given to the constants in the solution while drawing graphs representing the stationary wave. By making changes of these constants at certain intervals, the refraction dynamics and physical interpretations of the obtained internal solitary waves were included. These physical comments were supported by simulation with 3D, 2D and contour graphics. These two analytical methods used to obtain analytical solutions of the fractional Benjamin–Ono equation have been analyzed in detail by comparing their respective states. By using symbolic calculation, these methods have been shown to be the powerful and reliable mathematical tools for the solution of fractional nonlinear partial differential equations.

scholarly journals New and More Solitary Wave Solutions for the Klein-Gordon-Schrödinger Model Arising in Nucleon-Meson Interaction

2021 ◽  
Vol 9 ◽  
Author(s):  
Nauman Raza ◽  
Saima Arshed ◽  
Asma Rashid Butt ◽  
Dumitru Baleanu
Keyword(s):  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Art Integration ◽  
Scalar Mesons ◽  
Integration Schemes ◽  
Klein Gordon ◽  
Physical Features ◽  
Existence Criteria ◽  
Singular Soliton

This paper considers methods to extract exact, explicit, and new single soliton solutions related to the nonlinear Klein-Gordon-Schrödinger model that is utilized in the study of neutral scalar mesons associated with conserved scalar nucleons coupled through the Yukawa interaction. Three state of the art integration schemes, namely, the e−Φ(ξ)-expansion method, Kudryashov's method, and the tanh-coth expansion method are employed to extract bright soliton, dark soliton, periodic soliton, combo soliton, kink soliton, and singular soliton solutions. All the constructed solutions satisfy their existence criteria. It is shown that these methods are concise, straightforward, promising, and reliable mathematical tools to untangle the physical features of mathematical physics equations.

Optical solitons, complexitons, Gaussian soliton and power series solutions of a generalized Hirota equation

2018 ◽  
Vol 32 (14) ◽  
pp. 1850143 ◽  
Author(s):  
Jin-Jin Mao ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Dynamical Behavior ◽  
Soliton Solutions ◽  
Dark Soliton ◽  
Graphical Analysis ◽  
Optical Solitons ◽  
Series Solutions ◽  
Hirota Equation ◽  
Power Series Solutions ◽  
Propagation Properties

In this paper, we consider a generalized Hirota equation with a bounded potential, which can be used to describe the propagation properties of optical soliton solutions. By employing the hypothetical method and the sub-equation method, we construct the bright soliton, dark soliton, complexitons and Gaussian soliton solutions of the Hirota equation. Moreover, we explicitly derive the power series solutions with their convergence analysis. Finally, we provide the graphical analysis of such soliton solutions in order to better understand their dynamical behavior.

New optical soliton solutions of Biswas–Arshed model with Kerr law nonlinearity

2021 ◽  
pp. 2150263
Author(s):  
A. Tripathy ◽  
S. Sahoo ◽  
S. Saha Ray ◽  
M. A. Abdou
Keyword(s):  
Exact Solutions ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Dark Soliton ◽  
Optical Soliton ◽  
Wave Solutions ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Ode Method ◽  
Novel Methods

In this paper, the newly derived solutions for the optical soliton of Kerr law nonlinearity form of Biswas–Arshed model are investigated. The exact solutions are extracted by deploying two different novel methods namely, [Formula: see text]-expansion method and Riccati–Bernoulli sub-ODE method. Furthermore, in different conditions, the resultants show different wave solutions like singular, kink, anti-kink, periodic, rational, exponential and dark soliton solutions. Also, the dynamics of the attained solutions are presented graphically.

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.

Optical bright, dark and dipole solitons with derivative nonlinearity in the presence of parity-time-symmetric lattices

2020 ◽  
Vol 34 (16) ◽  
pp. 2050174
Author(s):  
Asad Zubair ◽  
Nauman Raza
Keyword(s):  
Nonlinear Medium ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Arbitrary Power ◽  
Derivative Term ◽  
Linear And Nonlinear ◽  
New Formula ◽  
Singular Soliton ◽  
Engineering Scheme

This paper deals with the study of optical solitons in the presence of new linear and nonlinear parity-time [Formula: see text]-symmetric modulation lattices. The nonlinear medium is a derivative term with arbitrary power. Inverse engineering scheme is utilized to retrieve bright, dark, dipole and singular soliton solutions. These solutions are presented for four new [Formula: see text]-symmetric potentials. The results reveal that optical bright, dark and dipole solitons can exist for those new physical settings.

Optical solitons in nonlinear directional couplers with G′/G-expansion scheme

2015 ◽  
Vol 24 (02) ◽  
pp. 1550017 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami ◽  
Qin Zhou ◽  
M. F. Mahmood ◽  
Essaid Zerrad ◽  
...  
Keyword(s):  
Power Law ◽  
Soliton Solutions ◽  
Nearest Neighbors ◽  
Optical Solitons ◽  
Nonlinear Media ◽  
Parabolic Law ◽  
Kerr Law ◽  
Singular Soliton ◽  
Optical Couplers ◽  
Expansion Scheme

This paper obtains soliton solutions in optical couplers. The governing equation is solved by the aid of G′/G-expansion scheme. There are four types of nonlinear media that are taken into consideration. These are Kerr law, power law, parabolic law, and dual-power law. There are two kinds optical couplers studied in this paper. They are twin-core couplers and multiple-core couplers, where coupling with nearest neighbors as well as coupling with all neighbors are considered. Dark and singular soliton solutions are retrieved. These soliton solutions come with constraint conditions that must hold for the solitons to exist.

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