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ISSN: 1558-6359 (Online)
Research Article Open Access

Integrability and Prolongation Structure of a Generalized Korteweg-de Vries Equation

Paul Bracken

Abstract

A closed differential ideal is constructed for a generalized Korteweg-de Vries equation. The ideal can be used to establish integrability for the equation. Some prolongation structures are determined for the equation and some larger prolongation algebras for given instances of the equation are found. The significance of this is that Backlund transformations can be developed based on them. It is shown how a Backlund transformation for a case of the equation can be formulated.

Journal of Mathematics and Statistics
Volume 6 No. 2, 2010, 125-130

DOI: https://doi.org/10.3844/jmssp.2010.125.130

Submitted On: 28 February 2010 Published On: 30 June 2010

How to Cite: Bracken, P. (2010). Integrability and Prolongation Structure of a Generalized Korteweg-de Vries Equation. Journal of Mathematics and Statistics, 6(2), 125-130. https://doi.org/10.3844/jmssp.2010.125.130

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 ideal
  • prolongation
  • Backlund transformation
  • symmetry group