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We transfer the scheme for constructing differential reductions recentlydeveloped for the Manakov-Santini hierarchy to the case of the two-componentgeneralization of dispersionless 2DTL hierarchy. We demonstrate that theequation arising as a result of the simplest reduction is equivalent (up to aLegendre type transformation) to the Dunajski-Tod equation, locally describinggeneral ASD vacuum metric with conformal symmetry. We consider higherreductions and corresponding reduced hierarchies also.

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