Arbeitsgruppe Geometrie

Mathematical Physics 3: Integrable Systems (WS 2015/2016)

This is a course of the Berlin Mathematical School held in English.

Office Hours: Wednesday, 14:00-15:00, MA 827

Script (hand-written, mainly in German)

• Introduction; first examples
• Hamiltonian dynamics
• Complete integrability, theorem of Liouville-Arnold, action-angle variables
• Poisson manifolds; Lie-Poisson bracket
• Lax equations, Lax representations
• Toda chain; solution in the open-end case (after Moser)
• Adler-Kostant-Symes scheme, kinematic and hamiltonian aspects
• Infinite Toda chain; inverse spectral method
• Korteweg-de Vries equation: algebraic theory, bi-hamiltonian structure, pseudo-differential operators, inverse spectral method