RT Journal Article
SR Electronic
T1 The prolongation structures of a class of nonlinear evolution equations
JF Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
JO Proc R Soc Lond A Math Phys Sci
FD The Royal Society
SP 411
OP 433
DO 10.1098/rspa.1978.0049
VO 359
IS 1699
A1
A1
YR 1978
UL http://rspa.royalsocietypublishing.org/content/359/1699/411.abstract
AB 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.