论文标题
关于偶数周期性链条的理性解决方案
On Rational Solutions of Dressing Chains of Even Periodicity
论文作者
论文摘要
我们开发了一种系统的方法来得出有理解决方案并获得其参数的分类，以使其均匀的链链或等效地$ a^{（1）} _ {n-1} $不变painlevé方程。该构造确定了有理解决方案，该解决方案具有作用于偶发性链条的一阶多项式解决方案的基本转移操作员轨道上的点。我们还获得了存在特殊函数解决方案的条件，这些解决方案是特殊类别的一阶多项式解决方案。 对于N = 4敷料链方程的特殊情况，该方法得出了PainlevéV方程的所有已知合理解决方案。它们是通过移动操作员对两个独立的一阶多项式解决方案的作用而获得的。正式主义自然地延伸至n = 6及以后，如论文所示。
We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalently $A^{(1)}_{N-1}$ invariant Painlevé equations. This construction identifies rational solutions with points on orbits of fundamental shift operators acting on first-order polynomial solutions derived for dressing chains of even periodicity. We also obtain conditions for the existence of special function solutions that occur for a special class of first-order polynomial solutions. For the special case of the N=4 dressing chain equations the method yields all the known rational solutions of Painlevé V equation. They are obtained through action of shift operators on the two independent first-order polynomial solutions. The formalism naturally extends to N=6 and beyond as shown in the paper.
