Involution analysis for nonlinear exterior differential systems

Abstract

Analysing auxiliary systems for integrability conditions is an indispensable part of many indirect studies of partial differential equations, such as symmetry analysis. An invariant differential geometric approach to integrability analysis is described, using the concept of an involutive exterior differential system. The essential theory is first presented, paying particular attention to the nonlinear case, and then algorithms implementing the central techniques are discussed.