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

Details 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

2007-01-15

arxiv.org/abs/nlin/0701029v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, IOP style

Scientific paper

10.1088/1751-8113/40/42/S11

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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