Last updated February 3, 2003
Geometry and algebra of partial differential equations

Part 1. Differential equations and finite jets.

  1. Manifolds and bundles of finite order jets.
  2. Cartan distribution and its integral manifolds.
  3. Automorphisms of the Cartan distribution. Lie-Baecklund theorem.
  4. Differential equations as submanifolds of jet manifolds.
  5. Classical symmetries.
  6. Examples of computations and applications of classical symmetries.

Part 2. Infinite jets and infinitely prolonged equations.

  1. Manifolds and bundles of infinite jets. Infinitely prolonged equations.
  2. Calculus on infinite jets.
  3. Connections and the Cartan distribution on infinite jets. Integral manifolds.
  4. Higher symmetries.
  5. C-differential operators.
  6. Horizontal cohomology and conservation laws.

Part 3. Nonlocal theory.

  1. Coverings in the category of differential equations.
  2. Wahlquist-Estabrook algebras.
  3. Nonlocal symmetries.
  4. Baecklund transformations. Bianchi formulas.
  5. Differential fundamental group.

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