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arXiv · 1204.3780

Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy

L. V. Bogdanov
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Abstract

We transfer the scheme for constructing differential reductions recently developed for the Manakov-Santini hierarchy to the case of the two-component generalization of dispersionless 2DTL hierarchy. We demonstrate that the equation arising as a result of the simplest reduction is equivalent (up to a Legendre type transformation) to the Dunajski-Tod equation, locally describing general ASD vacuum metric with conformal symmetry. We consider higher reductions and corresponding reduced hierarchies also.

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L. V. Bogdanov. 2012-04-17. Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy. https://doi.org/10.1016/j.physleta.2012.10.012

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