%0 Journal Article
%A
%A
%T The prolongation structures of a class of nonlinear evolution equations
%D 1978
%R 10.1098/rspa.1978.0049
%J Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
%P 411-433
%V 359
%N 1699
%X We show it is possible, by a simple process, to obtain prolongation structures of those equations solvable by the inverse method of Ablowitz, Kaup, Newell & Segur including the sine-Gordon, modified K .dV . and K. d V. equations. This follows the general procedure mapped out by Wahlquist & Estabrook. Furthermore, once a prolongation structure has been obtained, either by this method or individually from first principles, it is possible to deduce Backlund transformations from the invariance properties of the associated Lie algebras and the vector fields which these induce on a manifold naturally associated with the inverse scheme.
%U http://rspa.royalsocietypublishing.org/content/royprsa/359/1699/411.full.pdf