Superposition formulas for exterior differential systems

Abstract

In this article we solve an inverse problem in the theory of quotients for differential equations. We characterize a family of exterior differential systems that can be written as a quotient of a direct sum of two associated systems that are constructed from the original. The fact that a system can be written as a quotient can be used to find the general solution to these equations. Some examples are given to demonstrate the theory. © 2009 Elsevier Inc. All rights reserved.