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

doi:10.1088/1674-1056/19/8/080204

Abstract This paper applies the variational iteration method to obtain approximate analytic solutions of a generalized Hirota–Satsuma coupled Korteweg-de Vries (KdV) equation and a coupled modified Korteweg-de Vries (mKdV) equation. This method provides a sequence of functions which converges to the exact solution of the problem and is based on the use of the Lagrange multiplier for the identification of optimal values of parameters in a functional. Some examples are given to demonstrate the reliability and convenience of the method and comparisons are made with the exact solutions.

Keywords: approximate analytic solutions generalized Hirota–Satsuma coupled KdV equation coupled mKdV equation variational iteration method

Received: 14 December 2009
Revised: 22 January 2010
Accepted manuscript online:

PACS:	02.30.Xx	(Calculus of variations)
	02.30.Lt	(Sequences, series, and summability)
	02.30.Sa	(Functional analysis)
	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10771019 and 10826107).

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Zhao Guo-Zhong (赵国忠), Yu Xi-Jun (蔚喜军), Xu Yun (徐云), Zhu Jiang (朱江), Wu Di (吴迪) Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation 2010 Chin. Phys. B 19 080204

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

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