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Theoretical and Mathematical Physics

, Volume 167, Issue 3, pp 705–713 | Cite as

Interpolating differential reductions of multidimensional integrable hierarchies

  • L. V. BogdanovEmail author
Article

Abstract

We apply the scheme for constructing differential reductions recently developed for the Manakov-Santini hierarchy to the general multidimensional case. We consider the four-dimensional case connected with the second heavenly equation and its generalization proposed by Dunajski in more detail. We characterize differential reductions in terms of the Lax-Sato equations and also in the framework of the dressing method based on the nonlinear Riemann-Hilbert problem.

Keywords

multidimensional integrable hierarchy differential reduction Plebański equation 

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Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.Landau Institute for Theoretical PhysicsRASChernogolovka, Moscow OblastRussia

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