Journal of Mathematics and Statistics

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

Paul Bracken

DOI : 10.3844/jmssp.2010.125.130

Journal of Mathematics and Statistics

Volume 6, Issue 2

Pages 125-130


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.


© 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.