非线性Hill方程的对称群

The Symmetric Groups of a Class of Nonlinear Hill's Equations

研究一类非线性Hill方程 ,证明了其解的对称群的全体生成元构成一个三维Lie代数 ,并利用其对应线性Hill方程的基本解组得出了这个三维Lie代数其中一组基的表达式。

A class of nonlinear Hills equations which arises from the study of the generalized curve shortening problem is discussed. A result that the solution set of the equation admitting a three dimensional Lie algebra of infinitesimal symmetries is obtained.The basis of this algebra is also given in the following form2α i(x)x+α′ i(x)uu,i=0,1,2