论文标题
可集成链变量的不变流形和分离
Invariant manifolds and separation of the variables for integrable chains
论文作者
论文摘要
考虑到非线性集成晶格的广义不变流形的概念。早些时候，已经观察到，这种对象为评估递归操作员和宽松对的有效工具提供了有效的工具。在本文中，我们以一个volterra链的示例显示了广义不变的歧管也可用于构建精确的特定解决方案。为此，我们首先根据两个常数参数找到一个不变的歧管。然后，我们假设定义广义不变歧管的普通差方程取决于一个频谱参数之一，并为多项式的根而定于普通差和微分方程。该方法的效率由一些说明性示例批准。
A notion of the generalized invariant manifold for a nonlinear integrable lattice is considered. Earlier it has been observed that this kind objects provide an effective tool for evaluating the recursion operators and Lax pairs. In this article we show with an example of the Volterra chain that the generalized invariant manifold can be used for constructing exact particular solutions as well. To this end we first find an invariant manifold depending on two constant parameters. Then we assume that ordinary difference equation defining the generalized invariant manifold has a solution polynomially depending on one of the spectral parameters and derive ordinary difference and differential equations, for the roots of the polynomials. Efficiency of the method is approved by some illustrative examples.
