TY  - JOUR
AU  - Bracken, Paul 
PY  - 2010
TI  - Integrability and Prolongation Structure of a Generalized Korteweg-de Vries Equation
JF  - Journal of Mathematics and Statistics
VL  - 6
IS  - 2
DO  - 10.3844/jmssp.2010.125.130
UR  - https://thescipub.com/abstract/jmssp.2010.125.130
AB  - 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.