## 留言板

 引用本文: 张解放, 刘宇陆. 寻找具有三个任意函数的变系数KdV-MKdV方程的类孤波解的新方法[J]. 应用数学和力学, 2003, 24(11): 1114-1117.
ZHANG Jie-fang, LIU Yu-lu. New Truncated Expansion Method and Soliton-Like Solution of Variable Coefficient KdV-MKdV Equation With Three Arbitrary Functions[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1114-1117.
 Citation: ZHANG Jie-fang, LIU Yu-lu. New Truncated Expansion Method and Soliton-Like Solution of Variable Coefficient KdV-MKdV Equation With Three Arbitrary Functions[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1114-1117.

• 中图分类号: O175

## New Truncated Expansion Method and Soliton-Like Solution of Variable Coefficient KdV-MKdV Equation With Three Arbitrary Functions

• 摘要: 给出了求具有三个任意函数的变系数非线性演化方程的类孤波解的截断展开方法.这种方法的关键是首先把形式解设为几个待定函数的截断展开形式,从而可将变系数非线性演化方程转化为一组待定函数的代数方程,然后进一步给出容易积分的待定函数的常微分方程组,从而构造出相应的类孤波解.
•  [1] Chen Z X,Guo B Y,Xiang L W.Complete integrablity and analytic solutions of a KdV_type equation[J].Journal of Mathematical Physics,1990,31(12):2851-2855. [2] 楼森岳,阮航宇.变系数KdV方程和变系数MKdV方程的无穷多守恒律 [J].物理学报,1992,41 (2):182-187. [3] 朱佐农.含外力项的广义KdV的类孤波解[J].物理学报,1992,41(10):1561-1565. [4] 李翊神,朱国城.一个谱可变演化方程的对称[J].科学通报,1986,31(19):1449-1453. [5] Gazeau J P,Winternitz P.Symmetries of variable coefficient KdV equations[J].Journal of Mathematical Phy sics,1992,33(12):4087-4102. [6] 楼森岳.推广的Boussinesq方程和KdV方程Painlev性质,Bcklund变换和Lax对 [J].中国科学(A辑),1991,21(6):622-631. [7] ZHU Zuo_nong.On the KdV_type equation with variable coefficients [J].J ournal of Physics A:Mathem atical and Gener al,1995,28(19):5673-5684. [8] 阮航宇,陈一新.寻找变系数非线性方程精确解的新方法[J].物理学报,2000,49(2):177-180. [9] 文双春,徐文成,郭旗,等.变系数非线性Sch rdinger方程孤子的演化[J].中国科学 (A辑),27 (10):949-953. [10] XU Bao_zhi,ZHAO Shen_qi.Inverse scattering transformation for the variable coefficient sine_Gordon type equations[J].Applied Ma them atics_JCU,Ser B,1994,9(3):331-337. [11] LIU Xi_qiang.Exact solution of the variable coefficient KdV and SG type equations[J].Applied Mathema tics_JCU,Ser B,1998,13(1):25-30. [12] ZHEN Yu_kun,Chan W L.B cklund transformation for the non_isospectral and variable coefficient nonlinear Sch rdinger equation[J].Jour nal of Physics A:Ma them atical and Genera l,1989,22(5):441-449. [13] 闫振亚,张鸿庆.具有三个任意函数的变系数KdV_MKdV方程的精确类孤子解 [J].物理学报,1999,48(11):1957-1961. [14] 张解放,陈芳跃.截断展开方法和广义变系数KdV方程新的类孤波解[J].物理学报,2001,50(9):1648-1650.

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##### 出版历程
• 收稿日期:  2001-04-19
• 修回日期:  2003-05-20
• 刊出日期:  2003-11-15

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