The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and the complete sets of differential invariants for symmetry groups are found. The solution of the equivalence problem is given in terms of these invariants.
Contact Equivalence Problem for Nonlinear Wave Equations
Contact Equivalence Problem for Linear Hyperbolic Equations
Structure of Symmetry Groups via Cartan's Method: Survey of Four Approaches
