The Padé interpolation method applied to q-Painlevé equations II (differential grid version)

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• 作者：Hidehito Nagao
• 关键词：Padé method ; Padé interpolation ; q ; Painlevé equation
• 刊名：Letters in Mathematical Physics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：107
• 期：1
• 页码：107-127
• 全文大小：n>
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Complex Systems; Geometry; Group Theory and Generalizations;
• 出版者：Springer Netherlands
• ISSN：1573-0530
• 卷排序：107

文摘

Recently, we studied Padé interpolation problems of q-grid, related to q-Painlevé equations of type \(E_7^{(1)}\), \(E_6^{(1)}\), \(D_5^{(1)}\), \(A_4^{(1)}\) and \((A_2+A_1)^{(1)}\). By solving those problems, we could derive evolution equations, scalar Lax pairs and determinant formulae of special solutions for the corresponding q-Painlevé equations. It is natural that the q-Painlevé equations were derived by the interpolation method of q-grid, but it may be interesting in terms of differential grid that the Padé interpolation method of differential grid (i.e. Padé approximation method) has been applied to the q-Painlevé equation of type \(D_5^{(1)}\) by Ikawa. In this paper, we continue the above study and apply the Padé approximation method to the q-Painlevé equations of type \(E_6^{(1)}\), \(D_5^{(1)}\), \(A_4^{(1)}\) and \((A_2+A_1)^{(1)}\). Moreover, determinant formulae of the special solutions for q-Painlevé equation of type \(E_6^{(1)}\) are given in terms of the terminating q-Appell Lauricella function.