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 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 Gaussons: optical solitons with log-law nonlinearity by Laplace–Adomian decomposition method

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 182-188
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Abdullah Kamis Alzahrani
Keyword(s):  
Numerical Simulations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Decomposition Scheme ◽  
Error Analyses ◽  
Adomian Decomposition ◽  
Log Law

AbstractThis paper presents optical Gaussons by the aid of the Laplace–Adomian decomposition scheme. The numerical simulations are presented both in the presence and in the absence of the detuning term. The error analyses of the scheme are also displayed.

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.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

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

Bright and dark Thirring optical solitons with improved adomian decomposition method

Optik ◽  
2017 ◽  
Vol 130 ◽  
pp. 1115-1123 ◽  
Author(s):  
H.O. Bakodah ◽  
A.A. Al Qarni ◽  
M.A. Banaja ◽  
Qin Zhou ◽  
Seithuti P. Moshokoa ◽  
...  
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Adomian Decomposition

scholarly journals Cubic-quartic bright optical solitons with improved Adomian decomposition method

2020 ◽  
Vol 21 ◽  
pp. 161-167 ◽  
Author(s):  
O. González-Gaxiola ◽  
Anjan Biswas ◽  
Fouad Mallawi ◽  
Milivoj R. Belic
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Optical Solitons ◽  
Adomian Decomposition
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