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

Kenji Kajiwara; Marta Mazzocco; Yasuhiro Ohta

doi:10.1088/1751-8113/40/42/S11

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

Kenji Kajiwara, Marta Mazzocco, Yasuhiro Ohta

Division of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	12661-12675
Number of pages	15
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	40
Issue number	42
DOIs	https://doi.org/10.1088/1751-8113/40/42/S11
Publication status	Published - Oct 19 2007

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
Physics and Astronomy(all)

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10.1088/1751-8113/40/42/S11

Cite this

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AB - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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