On the one- And two-dimensional Toda lattices and the Painlevé property

J. D. Gibbon; M. Tabor

doi:10.1063/1.526863

On the one- And two-dimensional Toda lattices and the Painlevé property

J. D. Gibbon, M. Tabor

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

The Toda lattice and the two-dimensional Toda lattice (2-DTL) are shown to possess a type of "Painlevé property" that is based on the use of separate "singular manifolds" for each dependent variable. The isospectral problem for the 2-DTL found by both Mikhailov and by Fordy and Gibbons can be simply and logically derived from this analysis. Some remarks are made about the connection between our work and independent work of Kametaka and Airhault on the relationship between the Toda lattice and the second Painlevé transcendent.

Original language	English (US)
Pages (from-to)	1956-1960
Number of pages	5
Journal	Journal of Mathematical Physics
Volume	26
Issue number	8
DOIs	https://doi.org/10.1063/1.526863
State	Published - 1985
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.526863

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AU - Tabor, M.

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AB - The Toda lattice and the two-dimensional Toda lattice (2-DTL) are shown to possess a type of "Painlevé property" that is based on the use of separate "singular manifolds" for each dependent variable. The isospectral problem for the 2-DTL found by both Mikhailov and by Fordy and Gibbons can be simply and logically derived from this analysis. Some remarks are made about the connection between our work and independent work of Kametaka and Airhault on the relationship between the Toda lattice and the second Painlevé transcendent.

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On the one- And two-dimensional Toda lattices and the Painlevé property

Abstract

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