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.

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

  • Received Date: 2001-04-19
  • Rev Recd Date: 2003-05-20
  • Publish Date: 2003-11-15
  • The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.
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  • [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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