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齐次平衡原则及其应用
引用本文:王明亮,李志斌.齐次平衡原则及其应用[J].兰州大学学报(自然科学版),1999,35(3):8-16.
作者姓名:王明亮  李志斌
作者单位:[1]兰州大学数学系 [2]计算机科学系
摘    要:叙述齐次平衡原则及其在非线性数学物理中的应用:根据该原则可导出一大类非线性PDE的非线性变换,并借之得到方程的精确解;利用计算机的符号计算系数获得许多非线性PDE的弧立皮解;对一些非线性方程的边值-初值问题也可得到其精确解的表达式。

关 键 词:齐次平衡原则  非线性变换  精确解  偏微分方程

Homogeneous Balance Principle and Its Applications
Wang Mingliang ,Li Zhibin ,Zhou Yubin.Homogeneous Balance Principle and Its Applications[J].Journal of Lanzhou University(Natural Science),1999,35(3):8-16.
Authors:Wang Mingliang  Li Zhibin  Zhou Yubin
Institution:Wang Mingliang 1,Li Zhibin 2,Zhou Yubin 1
Abstract:The homogeneous balance principle and its applications in nonlinear mathematical physics are described:various nonlinear transformations for a large number of nonlinear PDEs are derived, by which the exact solutions of the corresponding nonlinear PDEs are obtained; the solitary wave solutions for numbers of nonlinear PDEs are acquired by using the symbolic computation system of a computer; the unique exact solution to the nonlinear boundary initial value problem of some nonlinear PDEs can be exactly expressed.
Keywords:homogeneous balance principle  nonlinear transformations  symbolic computation  nonlinear PDEs  boundary  initial value problems
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