Last updated October 12, 1999 |

(part IV, nonlocal theory)

For the previous courses see Geometry of nonlinear differential equations and Geometry of Differential Equations: Cohomological Aspects.

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

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