Abstract. The Boyer - Finley equation, or Toda equation is both a reduction of the self-dual Einstein equations and the dispersionless limit of the 2D Toda lattice equation. This suggests that there should be a dispersive version of the self-dual Einstein equation which both contains the Toda lattice equation and whose dispersionless limit is the familiar self-dual Einstein equation. Such a system is studied in this paper. The results are achieved by using a deformation, based on an associative -product, of the algebra used in the study of the undeformed, or dispersionless, equations.

Print publication: Issue 18 (21 September 1996)
Received 5 June 1996