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 TMF, 1994, Volume 99, Number 2, Pages 257–262 (Mi tmf1585)

Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants

E. V. Ferapontov

Institute for Mathematical Modelling, Russian Academy of Sciences

Abstract: We formulate several conjectures concerning the structure and general properties of the $n\times n$ integrable nondiagonalizable hamiltonian systems of hydrodynamic type. For $n=3$ our results are in fact complete: a $3\times 3$ nondiagonalizable hamiltonian system is integrable if and only if it is weakly nonlinear (linearly degenerate).

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English version:
Theoretical and Mathematical Physics, 1994, 99:2, 567–570

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Language: English

Citation: E. V. Ferapontov, “Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants”, TMF, 99:2 (1994), 257–262; Theoret. and Math. Phys., 99:2 (1994), 567–570

Citation in format AMSBIB
\Bibitem{Fer94} \by E.~V.~Ferapontov \paper Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants \jour TMF \yr 1994 \vol 99 \issue 2 \pages 257--262 \mathnet{http://mi.mathnet.ru/tmf1585} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1308787} \zmath{https://zbmath.org/?q=an:0851.58022} \transl \jour Theoret. and Math. Phys. \yr 1994 \vol 99 \issue 2 \pages 567--570 \crossref{https://doi.org/10.1007/BF01016140} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PV07100012} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. O. I. Mokhov, E. V. Ferapontov, “The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type”, Funct. Anal. Appl., 30:3 (1996), 195–203
2. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622
3. A. I. Zenchuk, “Solutions of multidimensional partial differential equations representable as a one-dimensional flow”, Theoret. and Math. Phys., 178:3 (2014), 299–313
4. Pavlov M.V., Vitolo R.F., “on the Bi-Hamiltonian Geometry of Wdvv Equations”, Lett. Math. Phys., 105:8 (2015), 1135–1163
5. Y. Kodama, B. G. Konopelchenko, “Confluence of hypergeometric functions and integrable hydrodynamic-type systems”, Theoret. and Math. Phys., 188:3 (2016), 1334–1357
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