Exact and numerical solitary wave solutions of generalized Zakharov equation by the Adomian decomposition method

2007 ◽  
Vol 32 (3) ◽  
pp. 1208-1214 ◽  
Author(s):  
Yue-yue Wang ◽  
Chao-qing Dai ◽  
Lei Wu ◽  
Jie-fang Zhang
Keyword(s):  
Solitary Wave ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Solitary Wave Solutions ◽  
Zakharov Equation ◽  
Wave Solutions ◽  
Adomian Decomposition

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 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 Analytical and semi analytical solutions of the internal waves of deep-stratified fluids

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 227-232
Author(s):  
Mostafa Khater ◽  
Raghda Attia ◽  
Sayed Elagan ◽  
Fatma Bayones
Keyword(s):  
Internal Waves ◽  
Analytical Solutions ◽  
Analytical Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Stratified Fluids ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Soliton Wave Solutions

In this paper, we study the soliton wave of the fractional Benjamin-Ono equation based on the extended simplest equation method. The accuracy of the obtained soliton wave solutions is investigated by comparing the obtained analytical and semi-analytical solutions. The semi-analytical solutions are constructed by applying the Adomian decomposition method. The semi-analytical method is used based on the constructed initial and boundary conditions from the obtained analytical solutions. Both solutions (analytical and semi-analytical) are plotted through different techniques for explaining the internal waves of deep-stratified fluids.

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