关于特征值问题的规范变换

Normal Transformation of the Eigenvalue Problem

本文指出了能用不含η的规范变换把特征值问题φx(-ηU+V)φ,φ=φ1φ2U=u1 u2u3 u4,V=vv31 vv42(1)化为下列一般形式的特征值问题Φx=(-ηU′+V′)Φ,Φ=ΦΦ21U′=-1-u0 1,V′=00 0v(2)的充要条件,并给出了规范变换及函数u,v的表达式,然后进一步说明了可以将(2)所对应的非线性发展方程化为(1)所对应的非线性发展方程。

In the paper,the necessary and sufficient condition for the eigenvalue problem φx(-ηU+V)φ,φ=φ1φ2U=u1 u2u3 u4,V=v1 v2v3 v4(1)to become the general eigenvalue problem φx=(-ηU′+V′)φ,φ=φ1φ2U′=-1-u 0 1,V′=0 v0 0(2)through normal transformation containing noη is pointed out and the expressionof normal transformation and the function u and v are given.Then further explained that the nonlinear evolution euqations corresponding to eigenvalue problem(2) can be transformed into nonlinear equations corresponding to eig...