Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-11-07
J.Math.Phys. 44 (2003) 3979-3999
Nonlinear Sciences
Exactly Solvable and Integrable Systems
LaTex2e, 30 pages, no figure (v2) an error in the beginning of Introduction corrected; (v3) typos and an error in eq. (73) cor
Scientific paper
10.1063/1.1591053
This paper presents a new approach to the Hamiltonian structure of isomonodromic deformations of a matrix system of ODE's on a torus. An isomonodromic analogue of the $\rmSU(2)$ Calogero-Gaudin system is used for a case study of this approach. A clue of this approach is a mapping to a finite number of points on the spectral curve of the isomonodromic Lax equation. The coordinates of these moving points give a new set of Darboux coordinates called the spectral Darboux coordinates. The system of isomonodromic deformations is thereby converted to a non-autonomous Hamiltonian system in the spectral Darboux coordinates. The Hamiltonians turn out to resemble those of a previously known isomonodromic system of a second order scalar ODE. The two isomonodromic systems are shown to be linked by a simple relation.
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