scholarly journals Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Anwar Ja’afar Mohamad Jawad ◽  
Mahmood Jawad Abu-AlShaeer
Keyword(s):  
Soliton Solution ◽  
Soliton Solutions ◽  
Boussinesq Equations ◽  
Optical Solitons ◽  
Equation Method ◽  
Practical Applications ◽  
Kerr Law ◽  
Simplest Equation Method ◽  
Kerr Law Nonlinearity ◽  
Modified Simple Equation Method

In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.

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.

A sub-equation method for solving the cubic–quartic NLSE with the Kerr law nonlinearity

2019 ◽  
Vol 33 (18) ◽  
pp. 1950197 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Ahmad Neirameh ◽  
Mostafa Eslami ◽  
Ahmet Bekir ◽  
Alper Korkmaz
Keyword(s):  
Exact Solutions ◽  
Optical Solitons ◽  
The Other ◽  
Equation Method ◽  
Kerr Law ◽  
Kerr Law Nonlinearity

In this paper, we study a class of cubic–quartic NLSE with the Kerr law nonlinearity via a new sub-equation method. Considered method of undetermined coefficients is applied to obtain the introduced solutions. The outcomes are useful in describing the diffusion of optical solitons. The performance of the approach is reliable, useful and gives more new general exact solutions than the other methods.

Optical soliton perturbation in magneto-optic waveguides

2018 ◽  
Vol 27 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Anjan Biswas ◽  
Ahmed H. Arnous ◽  
Mehmet Ekici ◽  
Abdullah Sonmezoglu ◽  
Aly R. Seadawy ◽  
...  
Keyword(s):  
Power Law ◽  
Optical Solitons ◽  
Simple Equation ◽  
Equation Method ◽  
Soliton Perturbation ◽  
Integration Schemes ◽  
Kerr Law ◽  
Logarithmic Law ◽  
Modified Simple Equation Method ◽  
Extended Trial

This paper addresses the dynamics of optical solitons in the presence of perturbation terms by the aid of three integration schemes. They are modified simple equation method, trial equation scheme, and the extended trial equation scheme. There are three types of nonlinearities that are studied in this paper which are Kerr law, power law, and logarithmic law. The constraint conditions for the existence of these solitons are also presented.

TOPOLOGICAL 1-SOLITON SOLUTION OF THE GENERALIZED RADHAKRISHNAN, KUNDU, LAKSHMANAN EQUATION WITH NONLINEAR DISPERSION

2010 ◽  
Vol 24 (16) ◽  
pp. 1825-1831 ◽  
Author(s):  
BENJAMIN STURDEVANT ◽  
DAWN A. LOTT ◽  
ANJAN BISWAS
Keyword(s):  
Solitary Wave ◽  
Power Law ◽  
Soliton Solution ◽  
Optical Solitons ◽  
Nonlinear Dispersion ◽  
Kerr Law

This paper talks about obtaining an exact 1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation with nonlinear dispersion. The solitary wave ansatz will be used to carry out the integration. It will be proved that dark optical solitons can exist only when the power law nonlinearity reduces to Kerr law.

scholarly journals New Soliton Solutions of the (2+1)-Dimensional System Davey-Stewartson Equation

2018 ◽  
Vol 7 (4.1) ◽  
pp. 37 ◽  
Author(s):  
Anwar J Ja'afar Mohamad Jawad ◽  
Mahmood J. Abu-Al Shaeer ◽  
Marko D. Petkovi_c
Keyword(s):  
Soliton Solutions ◽  
Travelling Wave ◽  
Simple Equation ◽  
Equation Method ◽  
Initial System ◽  
Wave Transformation ◽  
Dimensional System ◽  
Modified Simple Equation Method ◽  
Complex Coefficients

In this paper, we derive several soliton solutions of the generalized Davey-Stewartson equation with the complex coefficients. First we use the travelling wave transformation to reduce the initial system to ODE. The equivalent ODE is then solved, giving several classes of solutions, depending on the values of the parameters. Finally, the Extended Tanh-Coth method and Modified simple equation method.  

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.

Optical solitons for paraxial wave equation in Kerr media

2019 ◽  
Vol 33 (03) ◽  
pp. 1950020 ◽  
Author(s):  
Kashif Ali ◽  
Syed Tahir Raza Rizvi ◽  
Badar Nawaz ◽  
Muhammad Younis
Keyword(s):  
Wave Equation ◽  
Schrodinger Equation ◽  
Soliton Solutions ◽  
Optical Solitons ◽  
Equation Method ◽  
Kerr Media ◽  
Extended Trial Equation Method ◽  
Trial Equation Method ◽  
Paraxial Wave Equation ◽  
Extended Trial

This paper retrieves Jacobi elliptic, periodic, bright and singular solitons for paraxial nonlinear Schrödinger equation (NLSE) in Kerr media. We use extended trial equation method to obtain these solitons solutions. For the existence of the soliton solutions, constraint conditions are also presented.

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