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Teoreticheskaya i Matematicheskaya Fizika, 2017, Volume 191, Number 2, Pages 254–274
DOI: https://doi.org/10.4213/tmf9274 (Mi tmf9274) 		 
Integrable structures of dispersionless systems and differential geometry

A. V. Odesskii

Brock University, St. Catharines, Canada
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DOI: https://doi.org/10.4213/tmf9274
Abstract: 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 with the moduli space of algebraic curves of arbitrary genus and prove that the universal Whitham hierarchy is integrable by hydrodynamic reductions.
Keywords: integrability of quasilinear systems, hydrodynamic reduction, Gibbons–Tsarev system, Whitham-type hierarchy, moduli space of Riemann surfaces.
Received: 13.09.2016
Revised: 21.09.2016
English version:
Theoretical and Mathematical Physics, 2017, Volume 191, Issue 2, Pages 692–709
DOI: https://doi.org/10.1134/S0040577917050105
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Odesskii, “Integrable structures of dispersionless systems and differential geometry”, TMF, 191:2 (2017), 254–274; Theoret. and Math. Phys., 191:2 (2017), 692–709
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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