scholarly journals Solving Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

2021 ◽  
pp. 31-38
Author(s):  
Gaston Edah ◽  
Villévo Adanhoumè ◽  
Marc Amour Ayela
Keyword(s):  
Kerr Effect ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Initial Shape ◽  
The Third ◽  
Adomian Decomposition ◽  
Optical Cycle ◽  
Change Of Variable ◽  
Nonlinear Kerr Effect ◽  
Suitable Change

In this paper, using a suitable change of variable and applying the Adomian decomposition method to the generalized nonlinear Schr¨odinger equation, we obtain the analytical solution, taking into account the parameters such as the self-steepening factor, the second-order dispersive parameter, the third-order dispersive parameter and the nonlinear Kerr effect coefficient, for pulses that contain just a few optical cycle. The analytical solutions are plotted. Under influence of these effects, pulse did not maintain its initial shape.  

scholarly journals Pulse Propagation in a Non-Linear Medium

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Gaston Edah ◽  
Villévo Adanhounmè ◽  
Antonin Kanfon ◽  
François Guédjé ◽  
Mahouton Norbert Hounkonnou
Keyword(s):  
Pulse Propagation ◽  
Attenuation Factor ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Linear Medium ◽  
Novel Approach ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Change Of Variable ◽  
Suitable Change

AbstractThis paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium.

Measurement on the third-order optical nonlinearity of C70 and its poly-aminonitrile derivative by using the femtosecond optical Kerr effect

1999 ◽  
Vol 301 (3-4) ◽  
pp. 343-346 ◽  
Author(s):  
Tieqiao Zhang ◽  
Feng Wang ◽  
Hong Yang ◽  
Qihuang Gong ◽  
Xin An ◽  
...  
Keyword(s):  
Kerr Effect ◽  
Optical Nonlinearity ◽  
Optical Kerr Effect ◽  
Third Order ◽  
The Third

scholarly journals Temperature Dependent Viscosity of a Third Order Thin Film Fluid Layer on a Lubricating Vertical Belt

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
T. Gul ◽  
S. Islam ◽  
R. A. Shah ◽  
I. Khan ◽  
L. C. C. Dennis
Keyword(s):  
Thin Film ◽  
Variable Viscosity ◽  
Fluid Layer ◽  
Adomian Decomposition Method ◽  
Slip Boundary Condition ◽  
Thin Film Flow ◽  
Third Order ◽  
Temperature Dependent Viscosity ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition

This paper aims to study the influence of heat transfer on thin film flow of a reactive third order fluid with variable viscosity and slip boundary condition. The problem is formulated in the form of coupled nonlinear equations governing the flow together with appropriate boundary conditions. Approximate analytical solutions for velocity and temperature are obtained using Adomian Decomposition Method (ADM). Such solutions are also obtained by using Optimal Homotopy Asymptotic Method (OHAM) and are compared with ADM solutions. Both of these solutions are found identical as shown in graphs and tables. The graphical results for embedded flow parameters are also shown.

scholarly journals Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 335 ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Poom Kumam
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Fractional Order ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Third Order ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
In Series

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace–Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace–Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

Solution of the Magnetohydrodynamics Jeffery-Hamel Flow Equations by the Modified Adomian Decomposition Method

2015 ◽  
Vol 7 (5) ◽  
pp. 675-686 ◽  
Author(s):  
Lei Lu ◽  
Junsheng Duan ◽  
Longzhen Fan
Keyword(s):  
Decomposition Method ◽  
Nonlinear Boundary ◽  
Hartmann Number ◽  
Adomian Decomposition Method ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Equations ◽  
Analytical Approximations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

AbstractIn this paper, the nonlinear boundary value problem (BVP) for the Jeffery-Hamel flow equations taking into consideration the magnetohydrodynamics (MHD) effects is solved by using the modified Adomian decomposition method. We first transform the original two-dimensional MHD Jeffery-Hamel problem into an equivalent third-order BVP, then solve by the modified Adomian decomposition method for analytical approximations. Ultimately, the effects of Reynolds number and Hartmann number are discussed.

scholarly journals Treatment for third-order nonlinear differential equations based on the Adomian decomposition method

2017 ◽  
Vol 20 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Xueqin Lv ◽  
Jianfang Gao
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Adomian Decomposition Method ◽  
Differential Algebraic Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Algebraic Equations ◽  
Third Order ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

The Adomian decomposition method (ADM) is an efficient method for solving linear and nonlinear ordinary differential equations, differential algebraic equations, partial differential equations, stochastic differential equations, and integral equations. Based on the ADM, a new analytical and numerical treatment is introduced in this research for third-order boundary-value problems. The effectiveness of the proposed approach is verified by numerical examples.

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