A Remark on the Hankel Determinant Formula for Solutions of the Toda Equation

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Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality九州大学21世紀COEプログラム「機能数理学の構築と展開」We consider the Hankel determinant formula of the $ \tau $ functions ofthe Toda equation. We present a relationship between the determinant formulaand the auxiliary linear problem, which is characterized by a compact formula forthe $ \tau $ functions in the framework of the KP theory. Similar phenomena that havebeen observed for the Painleve II and IV equations are recovered. The case offinite lattice is also discussed.
2007-10-19