Last updated October 12, 1999
Geometry of differential equations
(part IV, nonlocal theory)
For the previous courses see Geometry of nonlinear differential equations and Geometry of Differential Equations: Cohomological Aspects.
A course program

  1. Basic differential-geometry structures in the theory of nonlinear partial differential equations (an overview).
  2. Origins and examples of nonlocal constructions in geometry of partial differential equations.
  3. Coverings in the category of differential equations. Definitions and basic constructions. Coverings and connections.
  4. Examples of coverings.
  5. Nonlocal symmetries and their shadows.
  6. Reconstruction theorem.
  7. Relations between coverings and horizontalcohomology and conservation laws. Universal Abelean covering and its properties.
  8. Action of classical symmetries on classes of coverings. Smooth families of coverings and their relation to hohomological deformation theory.
  9. Linear coverings and zero-curvature representations. Horizontal cohomology with coefficients.
  10. Baecklund transformations.
  11. Recursion operators for higher symmetries as Baecklund transformations.
  12. Problems and perspectives.

Questions and suggestions should go to J. S. Krasil'shchik, josephk @