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

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

2012-04-17

arxiv.org/abs/1204.3780v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages

Scientific paper

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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