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Research Article Open Access

Exterior Differential Systems for Higher Order Partial Differential Equations

Paul Bracken

Abstract

The theory of exterior differential systems is applied to study integrability of a set of related partial differential equations expressed in the terms of differential forms using Cartan's method. The Camassa-Holm equation and the Degasperis-Procesi equations are special cases that are described by these exterior differential systems. Some conservation laws are obtained in the cases of the more relevant equations. A closed differential ideal is constructed for each case studied.

Journal of Mathematics and Statistics
Volume 6 No. 1, 2010, 52-55

DOI: https://doi.org/10.3844/jmssp.2010.52.55

Submitted On: 25 January 2010 Published On: 31 March 2010

How to Cite: Bracken, P. (2010). Exterior Differential Systems for Higher Order Partial Differential Equations. Journal of Mathematics and Statistics, 6(1), 52-55. https://doi.org/10.3844/jmssp.2010.52.55

Open AccessCopyright: © 2010 Paul Bracken. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

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Keywords

  • Differential form
  • partial differential equation
  • integrability
  • Camassa-Holm