Electronic Journal of Differential Equations,
Conference 04 (2000), pp. 75-85.

Title: Twisting gravitational waves and eigenvector fields for 
 SL(2,C) on an infinite jet

Author: J. D. Finley, III (Univ. of New Mexico, Albuquerque, NM, USA)
 
Abstract: 
A system of coupled vector-field-valued partial differential 
equations is presented, the solutions to which would determine two coupled, 
infinite-dimensional vector-field realizations of the group SL(2,C). 
While the general solution is (partially) presented, the complicated 
nature of that solution is deplored, and the hope expressed that someone 
can replace it by something much more natural. The physical origins of the 
problem are briefly described. The problem arises out of searches for 
Backlund transforms of a system of PDE's that describe twisting, 
Petrov type N solutions of Einstein's vacuum field equations.

Published July 12, 2000.
Math Subject Classifications: 17B80, 37K10, 17B66, 83C35.
Key Words: Backlund transformations; Einstein equations; gravitational waves.