从第五Painlevé方程的Bäcklund变换导出的离散方程
Discrete equations from Bäcklund transformations of the fifth Painlevé equation
AI总结：
本文从第五Painlevé方程的Bäcklund变换导出离散方程，包括一个具有三元对称性的新离散方程，并利用广义Laguerre多项式和广义Umemura多项式推导出离散方程的有理解层次，同时利用非唯一有理解对得到满足同一离散方程的不同有理解层次。
摘要：
本文从第五Painlevé方程的Bäcklund变换导出了离散方程，包括一个具有三元对称性的新离散方程。第五Painlevé方程有两类有理解，一类用广义Laguerre多项式表示，另一类用广义Umemura多项式表示，两者均可表示为Laguerre多项式的Wronskian。利用广义Laguerre多项式和广义Umemura多项式导出了离散方程的有理解层次。已知第五Painlevé方程的一些有理解存在非唯一性。利用非唯一有理解对，得到了满足同一离散方程的不同有理解层次。
英文摘要：
In this paper discrete equations are derived from Bäcklund transformations of the fifth Painlevé equation, including a new discrete equation which has ternary symmetry. There are two classes of rational solutions of the fifth Painlevé equation, one expressed in terms of the generalised Laguerre polynomials and the other in terms of the generalised Umemura polynomials, both of which can be expressed as Wronskians of Laguerre polynomials. Hierarchies of rational solutions of the discrete equations are derived in terms of the generalised Laguerre and generalised Umemura polynomials. It is known that there is nonuniqueness of some rational solutions of the fifth Painlevé equation. Pairs of nonunique rational solutions are used to derive distinct hierarchies of rational solutions which satisfy the same discrete equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
