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- Title
On Some Hamiltonian Properties of the Isomonodromic Tau Functions.
- Authors
Its, A. R.; Prokhorov, A.
- Abstract
We discuss some new aspects of the theory of the Jimbo–Miwa–Ueno tau function which have come to light within the recent developments in the global asymptotic analysis of the tau functions related to the Painlevé equations. Specifically, we show that up to the total differentials the logarithmic derivatives of the Painlevé tau functions coincide with the corresponding classical action differential. This fact simplifies considerably the evaluation of the constant factors in the asymptotics of tau functions, which has been a long-standing problem of the asymptotic theory of Painlevé equations. Furthermore, we believe that this observation is yet another manifestation of L. D. Faddeev’s emphasis of the key role which the Hamiltonian aspects play in the theory of integrable system.
- Subjects
ISOMONODROMIC deformation method; DIFFERENTIAL equations; ASYMPTOTIC theory of algebraic ideals; HAMILTON'S principle function; ORDINARY differential equations; EIGENVALUES
- Publication
Reviews in Mathematical Physics, 2018, Vol 30, Issue 7, pN.PAG
- ISSN
0129-055X
- Publication type
Article
- DOI
10.1142/S0129055X18400081