Seminar talk, 16 December 2009

Speaker: Valery Yumaguzhin

Title: Structural differential invariants of natural bundles. Part 2. Geometric structures on solutions of nonlinear differential equations

Abstract:
Many of the nonlinear differential equations give rise to nontrivial geometric structures on their solutions viewed as manifolds. Differential invariants of these structures can be used in studying the solutions themselves.

In the talk the above claim will be demonstrated with examples of the system of adiabatic gas dynamics equations in $n$-dimensional space ($n=1,2,3$) and the Khokhlov-Zabolotskaya equation.

The talk is based on joint works of the speaker with Valentin Lychagin.