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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80204-080204.doi: 10.1088/1674-1056/19/8/080204

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

赵国忠¹, 吴迪¹, 朱江², 蔚喜军³, 徐云³

(1)Graduate School of China Academy of Engineering Physics, Beijing 100088, China; (2)Laborat'orio Nacional de Computacc ao Cientifica, MCT, Avenida Get'ulio Vargas 333, 25651-075 Petr'opolis, RJ, Brazil; (3)Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

收稿日期:2009-12-14 修回日期:2010-01-22 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10771019 and 10826107).

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

Zhao Guo-Zhong (赵国忠)^a, Yu Xi-Jun (蔚喜军)^b, Xu Yun (徐云)^b, Zhu Jiang (朱江)^c, Wu Di (吴迪)^a

^a Graduate School of China Academy of Engineering Physics, Beijing 100088, China; ^b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; ^c Laboratório Nacional de Computa??o Cientifica, MCT, Avenida Getúlio Vargas 333, 25651-075 Petrópolis, RJ, Brazil

Received:2009-12-14 Revised:2010-01-22 Online:2010-08-15 Published:2010-08-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 10771019 and 10826107).

摘要/Abstract

摘要： 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.

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.

Key words: approximate analytic solutions, generalized Hirota–Satsuma coupled KdV equation, coupled mKdV equation, variational iteration method

中图分类号: (Calculus of variations)

02.30.Xx

02.30.Lt (Sequences, series, and summability) 02.30.Sa (Functional analysis) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)

赵国忠, 蔚喜军, 徐云, 朱江, 吴迪. Approximate analytic solutions for a generalized Hirota–Satsuma coupled KdV equation and a coupled mKdV equation[J]. 中国物理B, 2010, 19(8): 80204-080204.

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[J]. Chin. Phys. B, 2010, 19(8): 80204-080204.

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

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

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