scholarly journals Adomian Decomposition Method for Approximating the Solution of the High-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

2006 ◽  
Vol 61 (5-6) ◽  
pp. 205-215 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Jian-Fei Luo
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Decomposition Method ◽  
Schrodinger Equation ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
High Order ◽  
Nonlinear Schrödinger ◽  
Adomian Decomposition ◽  
Quintic Nonlinear Schrödinger Equation

In this paper, the decomposition method is implemented for solving the high-order dispersive cubic-quintic nonlinear Schrödinger equation. By means of Maple the Adomian polynomials of obtained series solution have been calculated. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solutions of nonlinear problems. - PACS numbers: 02.30.Jr; 02.60.Cb; 42.65.Tg

scholarly journals Padé-Sumudu-Adomian Decomposition Method for Nonlinear Schrödinger Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Metomou Richard ◽  
Weidong Zhao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Decomposition Method ◽  
Schrodinger Equation ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Pade Approximation ◽  
Nonlinear Schrödinger ◽  
Adomian Decomposition

The main purpose of this paper is to solve the nonlinear Schrödinger equation using some suitable analytical and numerical methods such as Sumudu transform, Adomian Decomposition Method (ADM), and Padé approximation technique. In many literatures, we can see the Sumudu Adomian decomposition method (SADM) and the Laplace Adomian decomposition method (LADM); the SADM and LADM provide similar results. The SADM and LADM methods have been applied to solve nonlinear PDE, but the solution has small convergence radius for some PDE. We perform the SADM solution by using the function P L / M · called double Padé approximation. We will provide the graphical numerical simulations in 3D surface solutions of each application and the absolute error to illustrate the efficiency of the method. In our methods, the nonlinear terms are computed using Adomian polynomials, and the Padé approximation will be used to control the convergence of the series solutions. The suggested technique is successfully applied to nonlinear Schrödinger equations and proved to be highly accurate compared to the Sumudu Adomian decomposition method.

The Decomposition Method for Studying a Higher-Order Nonlinear Schrödinger Equation in Atmospheric Dynamics

2007 ◽  
Vol 62 (7-8) ◽  
pp. 387-395
Author(s):  
Zheng-Yi Ma
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Decomposition Method ◽  
Schrodinger Equation ◽  
Adomian Decomposition Method ◽  
Higher Order ◽  
Nonlinear Schrodinger Equation ◽  
Atmospheric Dynamics ◽  
Nonlinear Schrödinger ◽  
Adomian Decomposition

The Adomian decomposition method is implemented for solving a higher-order nonlinear Schrödinger equation in atmospheric dynamics. By means of Maple, the Adomian polynomials of an obtained series solution have been calculated. The results reported in this paper provide further evidence of the usefulness of Adomian decomposition for obtaining solutions of nonlinear problems.

scholarly journals An Approximate Analytical Solution of the Nonlinear Schrödinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Emad K. Jaradat ◽  
Omar Alomari ◽  
Mohammad Abudayah ◽  
Ala’a M. Al-Faqih
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schrödinger equation with harmonic oscillator. Accordingly, nonlinear Schrödinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function. The available literature does not provide an exact solution to the problem presented in this paper. Nevertheless, approximate analytical solutions are provided in this paper using LADM and HPM methods, in addition to comparing and analyzing both solutions.

scholarly journals Analytical Solutions to Generalized Nonlinear Schrödinger Equation by Adomian Decomposition Technique

2019 ◽  
pp. 1-11
Author(s):  
Villévo Adanhounme ◽  
Gaston Edah ◽  
Norbert M. Hounkonnou
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Propagation ◽  
Initial Condition ◽  
Nonlinear Schrödinger ◽  
Dispersion Effects ◽  
Adomian Decomposition

We study the higher-order nonlinear Schrödinger equation which takes care of the second as well as third order dispersion effects, cubic and quintic self phase modulations, self steepening and nonlinear dispersion effects. Taking advantage of the initial condition, we transform theprevious equation into a nonlinear functional equation to which we apply a powerful analytical method called the Adomian decomposition method. We compute the Adomian’s polynomials of corresponding infinite series solution. Assuming that the initial condition and all its derivatives converge to zero sufficiently rapidly as the time approaches to infinity, we established the convergence of the previous series. The last part of the paper describes applications resulting from nonlinear propagation phenomena in optical fibers. Numerical simulations are developed and it is further shown that comparison with other results yields a good qualitative agreement. These results demonstrate the robustness of the proposed method.

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