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Integrable structures of dispersionless systems and differential geometry

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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.

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Authors and Affiliations

  1. Brock University, St. Catharines, Canada

    A. V. Odesskii

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  1. A. V. Odesskii
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Correspondence to A. V. Odesskii.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 2, pp. 254–274, May, 2017.

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Odesskii, A.V. Integrable structures of dispersionless systems and differential geometry. Theor Math Phys 191, 692–709 (2017). https://doi.org/10.1134/S0040577917050105

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  • DOI: https://doi.org/10.1134/S0040577917050105

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