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

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arxiv nlin/0701029 v1 pith:EGNOH7MM submitted 2007-01-15 nlin.SI

Kenji Kajiwara , Marta Mazzocco , Yasuhiro Ohta This is my paper
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keywords formuladeterminantequationfunctionshankeltodaauxiliarybeen
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abstract

We consider the Hankel determinant formula of the $\tau$ 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 $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.

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  1. Two-dimensional Toda--Arnoldi correspondence: Holomorphic Krylov geometry and counterdiabatic transport

    quant-ph 2026-08 conditional novelty 5.0 of 10

    For non-Hermitian Hamiltonians, the Arnoldi diagonal and subdiagonal coefficients are the Flaschka variables of the finite two-dimensional Toda lattice, and their squares give both the Fubini-Study metric and the Berr...

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