A Remark on the Hankel Determinant Formula for Solutions of the Toda Equation
نویسندگان
چکیده
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. AMS classification scheme numbers: 37K10, 37K30, 34M55, 34M25, 34E05 Hankel determinant formula for the Toda equation 2
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Determinant Structure of the Rational Solutions for the Painlevé II Equation
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