论文标题
限制的TODA层次结构和对称径向Löwner方程的无分散版本
Dispersionless version of the constrained Toda hierarchy and symmetric radial Löwner equation
论文作者
论文摘要
我们研究了最近引入的受限TODA层次结构的无分散版本。像Toda晶格本身一样，它接受了三种等效的配方：根据宽松方程式的配方，Zakharov-Shabat类型的配方以及通过生成方程式制定的配方，以实现Tau功能的对数的分散极限。我们表明，无分散的限制TODA层次结构描述了对单位盘外部的反射对称平面域的共形图。我们还发现层次结构的有限维降低，并表明它们的特征是löwner类型的微分方程，我们称之为对称的径向Löwner方程。还表明，对称径向Löwner方程的解决方案是单位圆外部的共形图，并在单位圆的外部具有两个对称缝隙。
We study the dispersionless version of the recently introduced constrained Toda hierarchy. Like the Toda lattice itself, it admits three equivalent formulations: the formulation in terms of Lax equations, the formulation of the Zakharov-Shabat type and the formulation through the generating equation for the dispersionless limit of logarithm of the tau-function. We show that the dispersionless constrained Toda hierarchy describes conformal maps of reflection-symmetric planar domains to the exterior of the unit disc. We also find finite-dimensional reductions of the hierarchy and show that they are characterized by a differential equation of the Löwner type which we call the symmetric radial Löwner equation. It is also shown that solutions to the symmetric radial Löwner equation are conformal maps of the exterior of the unit circle with two symmetric slits to the exterior of the unit circle.
