The decomposition method for a Hirota–Satsuma coupled KdV equation and a coupled MKdV equation

2004 ◽  
Vol 81 (12) ◽  
pp. 1497-1505 ◽  
Author(s):  
K. R. Raslan
Keyword(s):  
Decomposition Method ◽  
Kdv Equation ◽  
Mkdv Equation ◽  
Coupled Kdv Equation

scholarly journals A New Solution of Time-Fractional Coupled KdV Equation by Using Natural Decomposition Method

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Mohamed Elbadri ◽  
Shams A. Ahmed ◽  
Yahya T. Abdalla ◽  
Walid Hdidi
Keyword(s):  
Decomposition Method ◽  
Kdv Equation ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Coupled Kdv Equation ◽  
A New Technique ◽  
Natural Decomposition ◽  
Made In

In this article, we applied a new technique for solving the time-fractional coupled Korteweg-de Vries (KdV) equation. This method is a combination of the natural transform method with the Adomian decomposition method called the natural decomposition method (NDM). The solutions have been made in a convergent series form. To demonstrate the performances of the technique, two examples are provided.

Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation

2010 ◽  
Vol 19 (8) ◽  
pp. 080204 ◽  
Author(s):  
Zhao Guo-Zhong ◽  
Yu Xi-Jun ◽  
Xu Yun ◽  
Zhu Jiang ◽  
Wu Di
Keyword(s):  
Kdv Equation ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Coupled Kdv Equation

scholarly journals Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jincun Liu ◽  
Hong Li
Keyword(s):  
Kdv Equation ◽  
Taylor Series Expansion ◽  
Analytic Solutions ◽  
Mkdv Equation ◽  
Differential Transform Method ◽  
Two Dimensional ◽  
Transform Method ◽  
Coupled Equations ◽  
Differential Transform ◽  
Coupled Kdv Equation

By introducing the fractional derivative in the sense of Caputo and combining the pretreatment technique to deal with long nonlinear items, the generalized two-dimensional differential transform method is proposed for solving the time-fractional Hirota-Satsuma coupled KdV equation and coupled MKdV equation. The presented method is a numerical method based on the generalized Taylor series expansion which constructs an analytical solution in the form of a polynomial. The numerical results show that the generalized two-dimensional differential transform method is very effective for the fractional coupled equations.

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