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TMF, 2017, Volume 191, Number 2, Pages 254–274 (Mi tmf9274)  

Integrable structures of dispersionless systems and differential geometry

A. V. Odesskii

Brock University, St. Catharines, Canada

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.

DOI: https://doi.org/10.4213/tmf9274

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English version:
Theoretical and Mathematical Physics, 2017, 191:2, 692–709

Bibliographic databases:

Received: 13.09.2016
Revised: 21.09.2016

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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