论文标题
有限的非周期性TODA晶格的扩展，具有无限度量
Extensions of the finite nonperiodic Toda lattices with indefinite metrics
论文作者
论文摘要
在本文中，我们首先构建了一个弱耦合的Toda晶格，该格子与不确定的指标由$ 2N $不同的耦合汉密尔顿系统组成。之后，我们考虑使用无限期指标的延长的三角形黑森贝格矩阵的异光谱歧管是什么是严格的三角形基质具有不确定指标的扩展。对于使用无限期指标的扩展对称TODA层次结构的初始值问题，我们通过使用Kodama的方法以特征值介绍了反向散射过程。在本文中，根据Szegö的正交程序，还讨论了$τ$ - 功能与给定的Lax矩阵之间的关系。我们可以使用一个简单的示例来验证从正交过程中得出的结果。之后，我们用无限期的指标构建了一个强烈的TODA晶格，并得出了其TAU结构。最后，我们将带有无限期指标的弱耦合的Toda晶格概括为$ z_ {n} $ - 带有无限期指标的toda lattices。
In this paper, we firstly construct a weakly coupled Toda lattices with indefinite metrics which consist of $2N$ different coupled Hamiltonian systems. Afterwards, we consider the iso-spectral manifolds of extended tridiagonal Hessenberg matrix with indefinite metrics what is an extension of a strict tridiagonal matrix with indefinite metrics. For the initial value problem of the extended symmetric Toda hierarchy with indefinite metrics, we introduce the inverse scattering procedure in terms of eigenvalues by using the Kodama's method. In this article, according to the orthogonalization procedure of Szegö, the relationship between the $τ$-function and the given Lax matrix is also discussed. We can verify the results derived from the orthogonalization procedure with a simple example. After that, we construct a strongly coupled Toda lattices with indefinite metrics and derive its tau structures. At last, we generalize the weakly coupled Toda lattices with indefinite metrics to the $Z_{n}$-Toda lattices with indefinite metrics.
