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

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Keywords

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