From continuous Painlevé IV to the asymmetric discrete Painlevé I
From continuous Painlevé IV to the asymmetric discrete Painlevé I
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DOI：
10.1088/0305-4470/31/27/009
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发表时间：
1998-07
期刊：
影响因子：
--
通讯作者：
B. Grammaticos;A. Ramani
中科院分区：
文献类型：
--
作者：
B. Grammaticos;A. Ramani
We examine the discrete equation that is obtained from the Schlesinger transformations of the continuous Painleve IV equation. The use of the Schlesinger transformations naturally establishes the Lax pair of the discrete equation which is an asymmetric form of d-P and has as continuous limit. We analyse the transformations of the discrete equation and show that they lead to a self-dual description where the discrete equation and the Schlesinger's play the same role. Finally, using the relation between and asymmetric d- we examine in detail the special solutions of both equations.
