Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
Exactly Solvable and Integrable Systems
2015-06-04 v2 General Relativity and Quantum Cosmology
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.
Keywords
Cite
@article{arxiv.1204.3780,
title = {Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy},
author = {L. V. Bogdanov},
journal= {arXiv preprint arXiv:1204.3780},
year = {2015}
}
Comments
14 pages, minor corrections, references added