The dispersive self-dual Einstein equations and the Toda lattice
Abstract
Description
The Boyer-Finley equation, or $SU(\infty)$-Toda equation is both a reduction of the self-dual Einstein equations and the dispersionlesslimit 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 $\star$-product, of the algebra $sdiff(Σ^2)$ used in the study of the undeformed, or dispersionless, equations.
11 pages, LaTeX. To appear: J. Phys. A
11 pages, LaTeX. To appear: J. Phys. A