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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
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
Linking options:
https://www.mathnet.ru/eng/tmf9274https://doi.org/10.4213/tmf9274 https://www.mathnet.ru/eng/tmf/v191/i2/p254
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Abstract page: | 293 | Full-text PDF : | 102 | References: | 53 | First page: | 22 |
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