"Integrable Systems"

Graduate course MAT 1052 HS, Spring 2016

Instructor: Prof. Boris Khesin
Time/location: Wed. and Fri. 11am-1pm at BA 6180.

  1. Billiards, symplectic structure on lines, Crofton's formula
  2. Integrability of the geodesic flow on an ellipsoid
  3. Hamiltonian systems, first integrals, the Arnold-Liouville theorem, tori
  4. Lie algebras, the Lie-Poisson bracket; example: a rigid body
  5. Bihamiltonian systems, the Lenard-Magri scheme, the Lax form; example: the Toda lattice
  6. Two Hamiltonian structures of the Korteweg-de Vries (KdV) equation
  7. The NLS and filament equations
  8. Introduction to the inverse scattering; example: KdV
  9. Introduction to solitons
  10. Near-integrability and non-integrability: glimps of the KAM and Arnold's diffusion
  11. Topics and generalizations (time permitted):
References: Prerequisite:

Some familiarity with the main notions of classical mechanics or symplectic geometry will be useful, but not required

Topics for mini-papers