scholarly journals Embedded solitons with χ(2) and χ(3) nonlinear susceptibilities

2021 ◽  
Vol 24 (02) ◽  
pp. 160-165
Author(s):  
Y. Yildirim ◽  
◽  
A. Biswas ◽  
S. Khan ◽  
M.R. Belic ◽  
...  
Keyword(s):  
Soliton Solutions ◽  
Quadratic Nonlinearity ◽  
Integration Schemes ◽  
Continuous Regime ◽  
Spatio Temporal ◽  
Existence Criteria ◽  
Singular Soliton ◽  
Temporal Dispersion

GStudied in this work are embedded solitons with quadratic nonlinearity that includes the effect of spatio-temporal dispersion. Two integration schemes yield bright, dark, singular and combo singular soliton solutions from the continuous regime. The existence criteria for these solitons are also included.

Optical solitons in DWDM system with spatio-temporal dispersion

2015 ◽  
Vol 24 (01) ◽  
pp. 1550006 ◽  
Author(s):  
M. Mirzazadeh ◽  
Mostafa Eslami ◽  
Michelle Savescu ◽  
A. H. Bhrawy ◽  
A. A. Alshaery ◽  
...  
Keyword(s):  
Soliton Solutions ◽  
Ansatz Method ◽  
Wavelength Division ◽  
Wavelength Division Multiplexed ◽  
Integration Algorithms ◽  
Spatio Temporal ◽  
Singular Soliton ◽  
Dwdm System ◽  
Temporal Dispersion ◽  
Expansion Scheme

This paper obtains bright, dark and singular soliton solutions to dense wavelength division multiplexed (DWDM) system, with spatio-temporal dispersion. There are two types of nonlinear media that are considered and they are Kerr law and parabolic law. Four integration algorithms are applied to retrieve these solitons. They are G′/G-expansion scheme, extended tanh function approach, Kudryashov's algorithm and finally the ansatz method. The results follow with respective constraints that guarantees the existence of solitons.

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 in Magneto-optic Waveguides with Spatio-temporal Dispersion

Frequenz ◽  
2014 ◽  
Vol 68 (9-10) ◽  
Author(s):  
Michelle Savescu ◽  
A. H. Bhrawy ◽  
E. M. Hilal ◽  
A. A. Alshaery ◽  
Anjan Biswas
Keyword(s):  
Soliton Solutions ◽  
Optical Solitons ◽  
Nonlinear Media ◽  
Kerr Law ◽  
Spatio Temporal ◽  
Ansatz Approach ◽  
The Ansatz Approach ◽  
Singular Soliton ◽  
Temporal Dispersion ◽  
Magneto Optic

AbstractThis paper obtains the exact solution for solitons propagating through magneto-optic waveguides. There are three forms of nonlinear media that are considered. They are Kerr law, power law and log-law nonlinearity. The ansatz approach retrieves bright, dark as well as singular soliton solutions. There are several constraint conditions that needs to be in place for the solitons and Gaussons to exist.

Soliton solutions to KdV equation with spatio-temporal dispersion

2016 ◽  
Vol 114 ◽  
pp. 192-203 ◽  
Author(s):  
Houria Triki ◽  
Turgut Ak ◽  
Seithuti Moshokoa ◽  
Anjan Biswas
Keyword(s):  
Kdv Equation ◽  
Soliton Solutions ◽  
Spatio Temporal ◽  
Temporal Dispersion

OPTICAL SOLITONS IN MULTI-DIMENSIONS WITH SPATIO-TEMPORAL DISPERSION AND NON-KERR LAW NONLINEARITY

2013 ◽  
Vol 22 (03) ◽  
pp. 1350035 ◽  
Author(s):  
YANAN XU ◽  
ZLATKO JOVANOSKI ◽  
ABDELAZIZ BOUASLA ◽  
HOURIA TRIKI ◽  
LUMINITA MORARU ◽  
...  
Keyword(s):  
Power Law ◽  
Necessary Conditions ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Parabolic Law ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Spatio Temporal ◽  
Ansatz Approach ◽  
Temporal Dispersion

This paper studies the dynamics of optical solitons in multi-dimensions with spatio-temporal dispersion and non-Kerr law nonlinearity. The integrability aspect is the main focus of this paper. Five different forms of nonlinearity are considered — Kerr law, power law, parabolic law, dual-power law and log law nonlinearity. The traveling wave hypothesis, ansatz approach and the semi-inverse variational principle are the integration tools that are adopted to retrieve the soliton solutions to the governing equation. As a result, several constraint conditions arise out of the integration process and represent necessary conditions for the existence of solitons.

Soliton solutions for Boussinesq-like equations with spatio-temporal dispersion

2017 ◽  
Vol 130 ◽  
pp. 228-240 ◽  
Author(s):  
M.T. Darvishi ◽  
M. Najafi ◽  
A.M. Wazwaz
Keyword(s):  
Soliton Solutions ◽  
Spatio Temporal ◽  
Temporal Dispersion

New exact optical soliton solutions for nonlinear Schrödinger equation with second-order spatio-temporal dispersion involving M-derivative

2019 ◽  
Vol 33 (20) ◽  
pp. 1950235 ◽  
Author(s):  
Behzad Ghanbari ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Function Method ◽  
Velocity Dispersion ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Mathematical Physics ◽  
Second Order ◽  
Dispersion Coefficients ◽  
Nonlinear Schrödinger ◽  
Spatio Temporal ◽  
Temporal Dispersion

This paper considers the generalized nonlinear Schrödinger (GNLS) equation with group velocity dispersion and second-order spatio-temporal dispersion coefficients. We obtain new dispersive solutions of a variety of GNLS equations via the exponential rational function method with the local M-derivative of order [Formula: see text]. The results obtained demonstrate that the employed method is simple and quite efficient for constructing exact solutions for other nonlinear equations arising in mathematical physics and nonlinear optics.

Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion

2017 ◽  
Vol 31 (14) ◽  
pp. 1750163 ◽  
Author(s):  
Mustafa Inc ◽  
Aliyu Isa Aliyu ◽  
Abdullahi Yusuf
Keyword(s):  
Conservation Laws ◽  
Soliton Solutions ◽  
Nonlinear Media ◽  
Parabolic Law ◽  
Kerr Law ◽  
Spatio Temporal ◽  
Schrödinger's Equation ◽  
Temporal Dispersion ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati–Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.

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