Symmetries of differential equations and Cartan's equivalence method

Abstract:
In this talk I will consider applications of Cartan's equivalence method to computing invariant forms and structure equations for symmetry groups of differential equations. This approach allows to find basic differential invariants and operators of invariant differentiation for symmetry groups without analysing over-determined systems of PDEs at all, and uses differentiation and linear algebra operations only. Examples will include contact equivalence problems for linear second-order parabolic equations, nonlinear wave equations, and the short wave gas dynamics equation.