Algorithms for Differential Invariants of Symmetry Groups of Differential Equations

We develop new computational algorithms, based on the method of equivariant moving frames, for classifying the differential invariants of Lie symmetry pseudo-groups of differential equations and analyzing the structure of the induced differential invariant algebra. The Korteweg–deVries (KdV) and Kadomtsev–Petviashvili (KP) equations serve as illustrate examples. In particular, we deduce the first complete classification of the differential invariants and their syzygies of the KP symmetry pseudo-group.