From Continuous to Discrete Painlevé Equations
From Continuous to Discrete Painlevé Equations
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DOI：
10.1006/jmaa.1993.1405
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发表时间：
1993-12
影响因子：
1.3
通讯作者：
A. Fokas;B. Grammaticos;A. Ramani
中科院分区：
文献类型：
--
作者：
A. Fokas;B. Grammaticos;A. Ramani
Painleve方程的离散类比最近已经用基于正交多项式的方法或奇点约束方法得到。在这里，我们分析了推导可积非自治离散方程的其他方法。这些方法基于离散AKNS方法，基于(连续)Painleve方程的Backlund和Schlesinger变换，以及Miura变换的离散类似物。
Abstract Discrete analogues of the Painleve equations have recently been derived using either a method based on orthogonal polynomials or the singularity confinement method. Here we analyze additional methods for deriving integrable non-autonomous discrete equations. These methods are based on the discrete AKNS approach, on the use of Backlund and Schlesinger transforms of the (continuous) Painleve equations, and on discrete analogues of Miura transformations.