Geodesic
Integrable structures of dispersionless systems and differential geometry
Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 254-274

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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. 
@article{TMF_2017_191_2_a9,
     author = {A. V. Odesskii},
     title = {Integrable structures of dispersionless systems and differential geometry},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {254--274},
     publisher = {mathdoc},
     volume = {191},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a9/}
}
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A. V. Odesskii. Integrable structures of dispersionless systems and differential geometry. Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 254-274. http://geodesic.mathdoc.fr/item/TMF_2017_191_2_a9/