The dispersive self-dual Einstein equations and the Toda lattice

Details The dispersive self-dual Einstein equations and the Toda lattice The dispersive self-dual Einstein equations and the Toda lattice

1996-06-17

arxiv.org/abs/hep-th/9606101v1

J.Phys.A29:6117-6124,1996

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, LaTeX. To appear: J. Phys. A

Scientific paper

10.1088/0305-4470/29/18/036

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 $sdiff(\Sigma^2)$ used in the study of the undeformed, or dispersionless, equations.

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