scholarly journals Numerical Solution of Dispersive Optical Solitons with Schrödinger-Hirota Equation by Improved Adomian Decomposition Method

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
H. O. Bakodah ◽  
M. A. Banaja ◽  
A. A. Alshaery ◽  
A. A. Al Qarni
Keyword(s):  
Decomposition Method ◽  
Group Velocity Dispersion ◽  
Soliton Solutions ◽  
Adomian Decomposition Method ◽  
Hirota Equation ◽  
Kerr Law ◽  
Adomian Decomposition ◽  
Spatio Temporal ◽  
High Level ◽  
Temporal Dispersion

In this paper, we present new numerical results for the dispersive optical soliton solutions of the nonlinear Schrödinger-Hirota equation. The spatio-temporal dispersion term is included, in addition to group velocity dispersion Kerr law of nonlinearity are studied. A general recursive numerical scheme for the equation is devised via the Improved Adomian Decomposition Method (IADM) and further sought for some analytical results for validation. The scheme is shown to be efficient and possessed high level of accuracy as demonstrated.

scholarly journals Highly dispersive optical solitons having Kerr law of refractive index with Laplace-Adomian decomposition

2020 ◽  
Vol 66 (3 May-Jun) ◽  
pp. 291 ◽  
Author(s):  
O. González Gaxiola ◽  
Anjan Biswas ◽  
Ali Saleh Alshomrani
Keyword(s):  
Refractive Index ◽  
Error Analysis ◽  
Decomposition Method ◽  
Soliton Solutions ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Bright Soliton ◽  
Kerr Law ◽  
Adomian Decomposition

This paper studies highly dispersive optical solitons, having Kerr law of refractive index, numerically. The adopted scheme is Laplace-Adomian decomposition method. Bright soliton solutions are displayed along with their respective error analysis.

scholarly journals The Greek parameters of a continuous arithmetic Asian option pricing model via Laplace Adomian decomposition method

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 780-785 ◽  
Author(s):  
Sunday O. Edeki ◽  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Grace O. Akinlabi
Keyword(s):  
Analytical Solution ◽  
Option Pricing ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Asian Option ◽  
Pricing Model ◽  
Adomian Decomposition ◽  
Option Pricing Model ◽  
Option Model ◽  
High Level

Abstract The Greek parameters in option pricing are derivatives used in hedging against option risks. In this paper, the Greeks of the continuous arithmetic Asian option pricing model are derived. The derivation is based on the analytical solution of the continuous arithmetic Asian option model obtained via a proposed semi-analytical method referred to as Laplace-Adomian decomposition method (LADM). The LADM gives the solution in explicit form with few iterations. The computational work involved is less. Nonetheless, high level of accuracy is not neglected. The obtained analytical solutions are in good agreement with those of Rogers & Shi (J. of Applied Probability 32: 1995, 1077-1088), and Elshegmani & Ahmad (ScienceAsia, 39S: 2013, 67–69). The proposed method is highly recommended for analytical solution of other forms of Asian option pricing models such as the geometric put and call options, even in their time-fractional forms. The basic Greeks obtained are the Theta, Delta, Speed, and Gamma which will be of great help to financial practitioners and traders in terms of hedging and strategy.

scholarly journals Numerical Simulation of Cubic-Quartic Optical Solitons with Perturbed Fokas–Lenells Equation Using Improved Adomian Decomposition Algorithm

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 138
Author(s):  
Alyaa A. Al-Qarni ◽  
Huda O. Bakodah ◽  
Aisha A. Alshaery ◽  
Anjan Biswas ◽  
Yakup Yıldırım ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Iterative Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Numerical Results ◽  
Decomposition Algorithm ◽  
Adomian Decomposition ◽  
High Level ◽  
Do So

The current manuscript displays elegant numerical results for cubic-quartic optical solitons associated with the perturbed Fokas–Lenells equations. To do so, we devise a generalized iterative method for the model using the improved Adomian decomposition method (ADM) and further seek validation from certain well-known results in the literature. As proven, the proposed scheme is efficient and possess a high level of accuracy.

Adomian Decomposition Method for Approximating the Solutions of the Bidirectional Sawada-Kotera Equation

2010 ◽  
Vol 65 (8-9) ◽  
pp. 658-664 ◽  
Author(s):  
Xian-Jing Lai ◽  
Xiao-Ou Cai
Keyword(s):  
Decomposition Method ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Absolute Error ◽  
Solitary Wave Solutions ◽  
Adomian Polynomials ◽  
Wave Solutions ◽  
Adomian Decomposition

In this paper, the decomposition method is implemented for solving the bidirectional Sawada- Kotera (bSK) equation with two kinds of initial conditions. As a result, the Adomian polynomials have been calculated and the approximate and exact solutions of the bSK equation are obtained by means of Maple, such as solitary wave solutions, doubly-periodic solutions, two-soliton solutions. Moreover, we compare the approximate solution with the exact solution in a table and analyze the absolute error and the relative error. The results reported in this article provide further evidence of the usefulness of the Adomian decomposition method for obtaining solutions of nonlinear problems

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.

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.

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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