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.

Received: 13.09.2016
Revised: 21.09.2016

DOI: 10.4213/tmf9274

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

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