Fractional sub-equation method for Hirota–Satsuma-coupled KdV equation and coupled mKdV equation using the Atangana’s conformable derivative

2018 ◽  
Vol 29 (4) ◽  
pp. 678-693 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J. F. Gómez-Aguilar
Keyword(s):  
Kdv Equation ◽  
Mkdv Equation ◽  
Equation Method ◽  
Conformable Derivative ◽  
Coupled Kdv Equation

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.

Multi-symplectic methods for the Ito-type coupled KdV equation

2012 ◽  
Vol 218 (9) ◽  
pp. 5552-5561 ◽  
Author(s):  
Yaming Chen ◽  
Songhe Song ◽  
Huajun Zhu
Keyword(s):  
Kdv Equation ◽  
Symplectic Methods ◽  
Coupled Kdv Equation
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