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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics