Integrable structures of dispersionless systems and differential geometry

Аннотация

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.