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

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.

14 pages, minor corrections, references added

References in corpus (3)

• Interpolating Dispersionless Integrable System
• The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
• A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields

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