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И.М.Кричевер

Интегрируемые системы

(ускоренный курс; начало 16 мая, 15.30, ком. 309)

Программа курса

1. Introduction. General features of the soliton systems.
   Lax representation. Zero-curvature equations. Discrete and finite-dimensional integrable systems. Integrals of motion. Hierarchies of commuting flows.
2. Algebro-geometric integration.
   Baker-Akhiezer functions. Theta-functional formulae. Baker-Akhiezer functions for singular curves (multisoliton solutions).
3. Spectral theory of periodic linear operators.
4. Hamiltonian theory of soliton equations.
5. Whitham equations and applications (WDVV equations, Witten-Seiberg theory)
6. Holomorphic vector bundles and solutions of higher rank.