两个非线性方程的势对称及其不变解  

Potential symmetries and invariant solutions of two nonlinear equations

作　　者：王晓民[1] 苏道毕力格[1] 

机构地区：[1]内蒙古工业大学理学院,内蒙古呼和浩特010051

出　　处：《量子电子学报》2016年第5期537-544,共8页Chinese Journal of Quantum Electronics

基　　金：国家自然科学基金;11571008;内蒙古自治区自然科学基金;2014MS0114;2014BS0105~~

摘　　要：通过计算非线性电报方程(NTT)和Burgers方程的势对称扩大了其古典对称,并获得了Burgers方程一系列新的精确解.基于微分特征列集算法确定了NTT方程和Burgers方程的古典对称和势对称,并计算了Burgers方程的2个势对称对应的单参数Lie变换群;利用推广的简单方程方法构造了Burgers方程的不变解,这些解分别以含任意2个参数的双曲函数、三角函数和有理函数表示;将势对称对应的Lie变换群(14)作用于Burgers方程的不变解获得了新的精确解,这些解都不能由方程的古典对称得到.The classical symmetries are expanded by calculating the potential symmetries of nonlinear telegraph-type（NTT） and Burgers equations,and a series of new exact solutions of Burgers equation are obtained.The classical symmetries and potential symmetries of NTT and Burgers equations are determined based on differential characteristic set algorithm,and one-parameter Lie transformation group of two potential symmetries to Burgers equation is calculated.The invariant solutions of Burgers equation are constructed by using generalized simple equation method,and these solutions are expressed by hyperbolic functions,trigonometric functions and rational functions with any two parameters respectively.New exact solutions are obtained by acting Lie transformation group（14） of potential symmetry on Burgers equation,and these solutions can＇t be obtained by the classical symmetry of the equation.

关 键 词：非线性方程 势对称 微分特征列集算法 非线性电报方程 BURGERS方程 不变解 

分 类 号：O175.29[理学—数学]