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arXiv · hep-th/9606101

The dispersive self-dual Einstein equations and the Toda lattice

I. A. B. Strachan
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Abstract

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.

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I. A. B. Strachan. 1996-06-17. The dispersive self-dual Einstein equations and the Toda lattice. https://doi.org/10.1088/0305-4470%2F29%2F18%2F036

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