Integrable structures of dispersionless systems and differential geometry

We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbons-Tsarev systems associated to moduli space of algebraic curves of arbitrary genus and prove that the universal Whitham...

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Bibliographic Details
Published in:arXiv.org 2016-09
Main Author: Odesskii, Alexander
Format: Article
Language:English
Subjects:
Differential geometry
Hierarchies
Online Access:Get full text
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Summary:We develop the theory of Whitham type hierarchies integrable by hydrodynamic reductions as a theory of certain differential-geometric objects. As an application we construct Gibbons-Tsarev systems associated to moduli space of algebraic curves of arbitrary genus and prove that the universal Whitham hierarchy is integrable by hydrodynamic reductions.
ISSN:2331-8422
DOI:10.48550/arxiv.1609.08969