Joseph Krasil'shchik's introductory lectures on the Geometry of Differential Equations

Autumn 2010

Lectures take place at the Independent University of Moscow on Wednesday evenings from 17:30 to 19:10 in room 206

The first lecture is on 15 September 2010

Short syllabus

• Jets of bundles
  The Cartan distribution
  Symmetries of the Cartan distribution
  The Lie-Bäcklund theorem

• Nonlinear differential equations and operators
  Classical symmetries of differential equations, their computation and application
  The Bianchi-Lie theorem

• Infinite jets and geometric structures on them
  The Cartan distribution on infinite jets and its symmetries
  Linearizations and evolutionary vector fields

• Prolongations of differential equations
  Infinitely prolonged equations
  Higher symmetries of differential equations, their computation and application
  Recursion operators for symmetries

Video records of the lectures

Via http://erb-files.narod.ru

• Lecture 1 (15 September 2010)

• Lecture 2 (22 September 2010)

• Lecture 3 (6 October 2010)

• Lecture 4 (20 October 2010)

Recommended literature

A. V. Bocharov, A. M. Verbovetsky, A. M. Vinogradov (editor), S. V. Duzhin, I. S. Krasil'shchik (editor), A. V. Samokhin, Yu. N. Torkhov, N. G. Khor'kova, and V. N. Chetverikov Simmetrii i zakony sokhraneniya uravnenij matematicheskoj fiziki, Factorial, Moscow, 2nd edition, 2005.

(English translation: Symmetries and conservation laws for differential equations of mathematical physics, AMS, 1999.)