scholarly journals New optical explicit plethora of the resonant Schrodinger’s equation via two recent computational schemes

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 247-255
Author(s):  
Mostafa Khater ◽  
Abdel-Haleem Abdel-Aty ◽  
Ghada Alnemer ◽  
Mohammed Zakarya ◽  
Dianchen Lu
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Research Paper ◽  
Linear Optics ◽  
Computational Schemes ◽  
Non Linear Optics ◽  
Wave Solutions ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Schrödinger's Equation

This research paper investigates the computational solutions of the resonant Schr?dinger?s equation. The modified Khater method and Adomian decomposition method are applyied for construct new analytical traveling and semi-analytical wave solutions. This model describes the pulse phenomena and studied in non-linear optics. For further illustration of our obtained solutions, some distinct types of sketches are given.

scholarly journals New optical explicit plethora of the resonant Schrodinger’s equation via two recent computational schemes

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 247-255
Author(s):  
Mostafa Khater ◽  
Abdel-Haleem Abdel-Aty ◽  
Ghada Alnemer ◽  
Mohammed Zakarya ◽  
Dianchen Lu
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Research Paper ◽  
Linear Optics ◽  
Computational Schemes ◽  
Non Linear Optics ◽  
Wave Solutions ◽  
Adomian Decomposition ◽  
Non Linear ◽  
Schrödinger's Equation

This research paper investigates the computational solutions of the resonant Schr?dinger?s equation. The modified Khater method and Adomian decomposition method are applyied for construct new analytical traveling and semi-analytical wave solutions. This model describes the pulse phenomena and studied in non-linear optics. For further illustration of our obtained solutions, some distinct types of sketches are given.

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

scholarly journals Approximate analytical solutions of non-linear local fractional heat equations

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 837-841 ◽  
Author(s):  
Shuxian Deng
Keyword(s):  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Heat Equations ◽  
Transform Method ◽  
Fractional Complex Transform ◽  
Fractional Heat Equation ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Non Linear

Consider the non-linear local fractional heat equation. The fractional complex transform method and the Adomian decomposition method are used to solve the equation. The approximate analytical solutions are obtained.

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