Applications of three methods for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model with Kerr law nonlinearity

Pramana ◽  
2020 ◽  
Vol 94 (1) ◽  
Author(s):  
Hadi Rezazadeh ◽  
Dipankar Kumar ◽  
Ahmad Neirameh ◽  
Mostafa Eslami ◽  
Mohammad Mirzazadeh
Keyword(s):  
Soliton Solutions ◽  
Optical Soliton ◽  
Kerr Law ◽  
Kerr Law Nonlinearity

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.

scholarly journals Optical soliton perturbation with spatio-temporal dispersion having Kerr law nonlinearity by the variational iteration method

2020 ◽  
Vol 66 (4 Jul-Aug) ◽  
pp. 404
Author(s):  
O. González Gaxiola ◽  
A. Biswas ◽  
A. Kamis Alzahrani ◽  
M. R. Belic
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Optical Soliton ◽  
Modal Dispersion ◽  
Soliton Perturbation ◽  
Variational Iteration ◽  
Kerr Law ◽  
Kerr Law Nonlinearity ◽  
Spatio Temporal ◽  
Temporal Dispersion

This paper studies optical soliton perturbation that appears with Kerr law nonlinearity having spatio-temporal dispersion. The numerical scheme adopted is the variational iteration method. The perturbation terms are of Hamiltonian type and stem from inter-modal dispersion, self-steepening and nonlinear dispersion. Both bright and dark solitons are taken into consideration.

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.

scholarly journals Optical soliton solutions of the Ginzburg-Landau equation with conformable conformable derivative and Kerr law nonlinearity

2018 ◽  
Vol 65 (1) ◽  
pp. 73 ◽  
Author(s):  
Francisco Gomez ◽  
Behzad Ghanbari
Keyword(s):  
Rational Function ◽  
Function Method ◽  
Landau Equation ◽  
Soliton Solutions ◽  
Conformable Derivative ◽  
Ginzburg Landau ◽  
Kerr Law ◽  
Ginzburg Landau Equation ◽  
Kerr Law Nonlinearity ◽  
Exponential Rational Function Method

By using the generalized exponential rational function method we obtain new periodic and hyperbolic soliton solutions for the conformable Ginzburg-Landau equation with Kerr law nonlinearity. The conformable derivative was considered to obtain the exact solutions under constraint conditions. To determine the solution of the model, the method uses the generalization of the exponential rational function method. Numerical simulations are performed to confirm the efficiency of the proposed method.

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.

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