Isomonodromic deformations in genus zero and one: algebrogeometric solutions and Schlesinger transformations

Details Isomonodromic deformations in genus zero and one: algebrogeometric solutions and Schlesinger transformations Isomonodromic deformations in genus zero and one: algebrogeometric solutions and Schlesinger transformations

2000-03-17

arxiv.org/abs/math-ph/0003016v1

Physics

Mathematical Physics

to appear in CRM publications, ed. by G.Sabidussi, AMS, 2000

Scientific paper

Here we review some recent developments in the theory of isomonodromic
deformations on Riemann sphere and elliptic curve. For both cases we show how
to derive
Schlesinger transformations together with their action on tau-function, and
construct classes of solutions in terms of multi-dimensional theta-functions.

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