Kenji Kajiwara et al 2007 J. Phys. A: Math. Theor. 40 12661 doi:10.1088/1751-8113/40/42/S11
A remark on the Hankel determinant formula for solutions of the Toda equation
Kenji Kajiwara1, Marta Mazzocco2 and Yasuhiro Ohta3
Show affiliationsWe 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.
- PACS
- MSC
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37K30 Relations with infinite-dimensional Lie algebras and other algebraic structures
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (See also 30E15)
34M55 Painlevé and other special equations; classification, hierarchies; isomonodromic deformations
- Subjects
- Dates
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Issue 42 (19 October 2007)
Received 15 January 2007, in final form 8 May 2007
Published 2 October 2007
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A remark on the Hankel determinant formula for solutions of the Toda equation
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