Integrability and Prolongation Structure of a Generalized Korteweg-de Vries Equation
Paul Bracken
Journal of Mathematics and Statistics, Volume 6, Issue 2, pp. 125–130 · doi.org/10.3844/jmssp.2010.125.130
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.
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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
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