论文标题
关于线性哈密顿系统的变形
On the deformation of linear Hamiltonian systems
论文作者
论文摘要
对于线性汉密尔顿$ 2N \ times 2n $ systems $ j y'（x）=（λw（x）+h（x））y（x）$我们调查了问题的特征值$λ$如何取决于系数矩阵$ h $的条目。这个问题变成了$ h $的变形方程和特征值$λ$的部分微分方程。我们将结果应用于各种示例，包括汇合HEUN方程和Chandrasekhar-Page角方程的概括。我们主要关注$ 2 \ times 2 $案例，为了尽可能降低$ h $中的自由度，我们将首先将此类系统转换为互补的三角形形式，这是一种规范的形式，具有最低数量的免费参数。此外，我们讨论了与单一保留变形和基质lax对的关系。
For linear Hamiltonian $2n\times 2n$ systems $J y'(x) = (λW(x)+H(x))y(x)$ we investigate the problem how the eigenvalues $λ$ depend on the entries of the coefficient matrix $H$. This question turns into a deformation equation for $H$ and a partial differential equation for the eigenvalues $λ$. We apply our results to various examples, including generalizations of the confluent Heun equation and the Chandrasekhar-Page angular equation. We are mainly concerned with the $2\times 2$ case, and in order to reduce the degrees of freedom in $H$ as much as possible, we will first convert such systems into a complementary triangular form, which is a canonical form with a minimum number of free parameters. Furthermore, we discuss relations to monodromy preserving deformations and to matrix Lax pairs.
