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A new method of constructing structure equations of Lie symmetry pseudo-groups of differential equations, dispensing with explicit solutions of the (infinitesimal) determining systems of the pseudo-groups, is presented, and illustrated by the examples of the Kadomtsev–Petviashvili and Korteweg–de-Vries 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… (More)
We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in G-spaces, whether homogeneous or not, provided that a certain k order jet bundle over the G-space admits a G-invariant local coframe field of constant structure. As a corollary, we note that the differential… (More)