Submitted by prime on
Title: Solving initial and boundary value problems using differential geometric techniques
Speaker: Professor Geoff Prince, La Trobe University, Melbourne
The jet bundle formulation of differential equations is used to express ideas of invariance of solutions of initial and boundary value problems. I show how to construct such invariant solutions from a knowledge of the symmetry group of the differential equations unconstrained by initial and boundary conditions. For example, given a system of second order ODEs on $\mathbb{R}^n$ and an initial distribution of tangent vectors we look for symmetries of the resulting congruence of solutions and, in the best situation, enough of them to explicitly integrate the congruence.