Maurer–Cartan equations for Lie symmetry pseudogroups of differential equations

Abstract

A new method of constructing structure equations of Lie symmetry pseudogroups of differential equations, dispensing with explicit solutions of the (infinitesimal) determining systems of the pseudogroups, is presented, and illustrated by the examples of the Kadomtsev–Petviashvili and Korteweg–de Vries equations.