论文标题
一个2组分的Camassa-Holm方程，Euler-Bernoulli梁问题和非交通性续分
A 2-component Camassa-Holm equation, Euler-Bernoulli Beam Problem and Non-Commutative Continued Fractions
论文作者
论文摘要
提出了一种基于不均匀矩阵弦问题的Euler-Bernoulli光束的新方法。该方法的三个后果是开发的：（1）由与Camassa-Holm方程的类比进行了类比，提出了一类光束问题的同一光谱变形； （2）根据某个紧凑型操作员的重新重新制定了矩阵字符串问题的重新制定，以获取具有Dirichlet边界条件的不均匀矩阵字符串问题的基本光谱特性； （3）对于离散的Euler-Bernoulli梁的特殊情况，解决了反问题。该解决方案涉及对Stieltjes的持续分数的非交通概括，从而导致根据Hankel样决定因素的比率表示反向公式。
A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed: (1) motivated by an analogy with the Camassa-Holm equation a class of isospectral deformations of the beam problem is formulated; (2) a reformulation of the matrix string problem in terms of a certain compact operator is used to obtain basic spectral properties of the inhomogeneous matrix string problem with Dirichlet boundary conditions; (3) the inverse problem is solved for the special case of a discrete Euler-Bernoulli beam. The solution involves a non-commutative generalization of Stieltjes' continued fractions, leading to the inverse formulas expressed in terms of ratios of Hankel-like determinants.
