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