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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 504645, 8 pages
http://dx.doi.org/10.1155/2013/504645
Research Article

Geometric Methods to Investigate Prolongation Structures for Differential Systems with Applications to Integrable Systems

Department of Mathematics, University of Texas, Edinburg, TX 78541-2999, USA

Received 8 January 2013; Accepted 13 February 2013

Academic Editor: Aloys Krieg

Copyright © 2013 Paul Bracken. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A type of prolongation structure for several general systems is discussed. They are based on a set of one forms for which the underlying structure group of the integrability condition corresponds to the Lie algebra of , , and . Each will be considered in turn and the latter two systems represent larger cases. This geometric approach is applied to all of the three of these systems to obtain prolongation structures explicitly. In both cases, the prolongation structure is reduced to the situation of three smaller problems.