Superposition Formulas for Darboux Integrable Exterior Differential Sys-tems
Published by Elsevier in Advances in Mathematics. Authors post print deposited in arXiv.org under title Superposition Formulas for Darboux Integrable Exterior Differential Systems and is available for download through link above.
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.
Ian M. Anderson, Mark E. Fels, Peter J. Vassiliou, Superposition formulas for exterior differential systems, Advances in Mathematics, Volume 221, Issue 6, 20 August 2009, Pages 1910-1963, ISSN 0001-8708, 10.1016/j.aim.2009.03.010.