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Theoretical and Mathematical Physics

, Volume 160, Issue 1, pp 887–893 | Cite as

A class of multidimensional integrable hierarchies and their reductions

  • L. V. Bogdanov
Article

Abstract

We consider a class of multidimensional integrable hierarchies connected with the commutativity of general (unreduced) (N+1)-dimensional vector fields containing a derivative with respect to a spectral variable. These hierarchies are determined by a generating equation, equivalent to the Lax-Sato form. We present a dressing scheme based on a nonlinear vector Riemann problem for this class. As characteristic examples, we consider the hierarchies connected with the Manakov-Santini equation and the Dunajski system.

Keywords

integrable hierarchy dispersionless equation heavenly equation dressing method 

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Copyright information

© MAIK/Nauka 2009

Authors and Affiliations

  1. 1.Landau Institute of Theoretical PhysicsRASMoscowRussia

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