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

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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 99, Number 2, Pages 257–262 (Mi tmf1585)

This article is cited in 13 scientific papers (total in 13 papers)

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

Full-text PDF (621 kB) Citations (13)

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Abstract: We formulate several conjectures concerning the structure and general properties of the

n \times n

$n\times n$ integrable nondiagonalizable hamiltonian systems of hydrodynamic type. For

n = 3

$n=3$ our results are in fact complete: a

3 \times 3

$3\times 3$ nondiagonalizable hamiltonian system is integrable if and only if it is weakly nonlinear (linearly degenerate).

English version:
Theoretical and Mathematical Physics, 1994, Volume 99, Issue 2, Pages 567–570
DOI: https://doi.org/10.1007/BF01016140

Bibliographic databases:

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

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\pages 567--570

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Linking options:

https://www.mathnet.ru/eng/tmf1585

https://www.mathnet.ru/eng/tmf/v99/i2/p257

This publication is cited in the following 13 articles:

R. Camassa, G. Falqui, G. Ortenzi, M. Pedroni, T. T. Vu Ho, “Hamiltonian Aspects of Three-Layer Stratified Fluids”, J Nonlinear Sci, 31:4 (2021)
Maxim V. Pavlov, Nikola M. Stoilov, “The WDVV Associativity Equations as a High-Frequency Limit”, J Nonlinear Sci, 28:5 (2018), 1843
Y. Kodama, B. G. Konopelchenko, “Confluence of hypergeometric functions and integrable hydrodynamic-type systems”, Theoret. and Math. Phys., 188:3 (2016), 1334–1357
Pavlov M.V., Vitolo R.F., “on the Bi-Hamiltonian Geometry of Wdvv Equations”, Lett. Math. Phys., 105:8 (2015), 1135–1163
O. Chvartatskyi, F. Müller-Hoissen, N. Stoilov, ““Riemann equations” in bidifferential calculus”, Journal of Mathematical Physics, 56:10 (2015)
A. I. Zenchuk, “Solutions of multidimensional partial differential equations representable as a one-dimensional flow”, Theoret. and Math. Phys., 178:3 (2014), 299–313
A.I. Zenchuk, “Particular solutions to multidimensional PDEs with KdV-type nonlinearity”, Physics Letters A, 378:14-15 (2014), 999
A. I. Zenchuk, “On integration of a multidimensional version of n-wave type equation”, Journal of Mathematical Physics, 55:12 (2014)
A.I. Zenchuk, “A modification of the method of characteristics: A new class of multidimensional partially integrable nonlinear systems”, Physics Letters A, 375:28-29 (2011), 2704
P.M. Santini, A.I. Zenchuk, “The general solution of the matrix equation”, Physics Letters A, 368:1-2 (2007), 48
T.A. Ivanova, A.D. Popov, “On Symmetries of Chern-Simons and BF Topological Theories”, JNMP, 7:4 (2000), 480
O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622
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

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

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References:	80
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