Solitary wave solutions for the general KDV equation by Adomian decomposition method

2004 ◽  
Vol 154 (1) ◽  
pp. 17-29 ◽  
Author(s):  
Hassan N.A Ismail ◽  
Kamal R Raslan ◽  
Ghada S.E Salem
Keyword(s):  
Solitary Wave ◽  
Decomposition Method ◽  
Kdv Equation ◽  
Adomian Decomposition Method ◽  
Solitary Wave Solutions ◽  
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

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