A remark on the Hankel determinant formula for solutions of the Toda equation

A remark on the Hankel determinant formula for solutions of the Toda equation
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DOI：
10.1088/1751-8113/40/42/s11
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发表时间：
2007-01
期刊：
Journal of Physics A: Mathematical and Theoretical
影响因子：
--
通讯作者：
K. Kajiwara;M. Mazzocco;Y. Ohta
K. Kajiwara;M. Mazzocco;Y. Ohta
中科院分区：
其他
文献类型：
--
作者：
K. Kajiwara;M. Mazzocco;Y. Ohta

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本文研究了户田方程τ函数的Hankel行列式公式。在KP理论的框架下，给出了行列式公式与辅助线性问题之间的关系，并给出了τ函数的一个紧公式.已观察到的Painlevé II和IV方程的类似现象被恢复。有限格的情况也进行了讨论。
We consider the Hankel determinant formula of the τ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the τ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlevé II and IV equations are recovered. The case of finite lattice is also discussed.