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Funktsional. Anal. i Prilozhen., 1996, Volume 30, Issue 3, Pages 62–72 (Mi faa538)  

This article is cited in 29 scientific papers (total in 29 papers)

The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type

O. I. Mokhova, E. V. Ferapontovb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute for Mathematical Modelling, Russian Academy of Sciences

DOI: https://doi.org/10.4213/faa538

Full text: PDF file (881 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 1996, 30:3, 195–203

Bibliographic databases:

UDC: 517.9+514.7
Received: 15.05.1995

Citation: O. I. Mokhov, E. V. Ferapontov, “The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian Nondiagonalizable Systems of Hydrodynamic Type”, Funktsional. Anal. i Prilozhen., 30:3 (1996), 62–72; Funct. Anal. Appl., 30:3 (1996), 195–203

Citation in format AMSBIB
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\by O.~I.~Mokhov, E.~V.~Ferapontov
\paper The Associativity Equations in the Two-Dimensional Topological Field Theory as Integrable Hamiltonian
Nondiagonalizable Systems of Hydrodynamic Type
\jour Funktsional. Anal. i Prilozhen.
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\issue 3
\pages 62--72
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\jour Funct. Anal. Appl.
\yr 1996
\vol 30
\issue 3
\pages 195--203
\crossref{https://doi.org/10.1007/BF02509506}
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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. S. I. Agafonov, E. V. Ferapontov, “Systems of conservation laws in the context of the projective theory of congruences”, Izv. Math., 60:6 (1996), 1097–1122  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Ferapontov, EV, “Bi-Hamiltonian structure of equations of associativity in 2-d topological field theory”, Communications in Mathematical Physics, 186:3 (1997), 649  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. Kalayci, J, “Bi-Hamiltonian structure of a WDVV equation in 2-d topological field theory”, Physics Letters A, 227:3–4 (1997), 177  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. O. I. Mokhov, “Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems”, Russian Math. Surveys, 53:3 (1998), 515–622  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Agafonov, SI, “Linearly degenerate reducible systems of hydrodynamic type”, Journal of Mathematical Analysis and Applications, 222:1 (1998), 15  crossref  mathscinet  zmath  isi
    6. Kalayci, J, “Alternative bi-Hamiltonian structures for WDVV equations of associativity”, Journal of Physics A-Mathematical and General, 31:2 (1998), 723  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    7. O. I. Mokhov, “Compatible Poisson Structures of Hydrodynamic Type and Associativity Equations”, Proc. Steklov Inst. Math., 225 (1999), 269–284  mathnet  mathscinet  zmath
    8. Mokhov, O, “Compatible Poisson structures of hydrodynamic type and the equations of associativity in two-dimensional topological field theory”, Reports on Mathematical Physics, 43:1–2 (1999), 247  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Ferapontov, EV, “Invariant description of solutions of hydrodynamic-type systems in hodograph space: hydrodynamic surfaces”, Journal of Physics A-Mathematical and General, 35:32 (2002), 6883  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Ferapontov, EV, “Hypersurfaces with flat centroafine metric and equations of associativity”, Geometriae Dedicata, 103:1 (2004), 33  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Conte, R, “Symmetry reductions of a particular set of equations of associativity in two-dimensional topological field theory”, Journal of Physics A-Mathematical and General, 38:5 (2005), 1187  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. M. V. Pavlov, “Integrability of the Egorov systems of hydrodynamic type”, Theoret. and Math. Phys., 150:2 (2007), 225–243  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. Sergyeyev, A, “Infinite hierarchies of nonlocal symmetries of the Chen-Kontsevich-Schwarz type for the oriented associativity equations”, Journal of Physics A-Mathematical and Theoretical, 42:40 (2009), 404017  crossref  mathscinet  zmath  isi
    14. O. I. Mokhov, “Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type”, Theoret. and Math. Phys., 167:1 (2011), 403–420  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    15. Agafonov S.I., “Flat 3-webs via semi-simple Frobenius 3-manifolds”, J Geom Phys, 62:2 (2012), 361–367  crossref  mathscinet  zmath  adsnasa  isi  elib
    16. A. M. Verbovetsky, R. Vitolo, P. Kersten, I. S. Krasil'shchik, “Integrable structures for a generalized Monge–Ampère equation”, Theoret. and Math. Phys., 171:2 (2012), 600–615  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    17. Sergey I. Agafonov, “Frobenius 3-folds via singular flat 3-webs”, SIGMA, 8 (2012), 078, 15 pp.  mathnet  crossref  mathscinet
    18. Ferapontov E.V., Pavlov M.V., Vitolo R.F., “Projective-Geometric Aspects of Homogeneous Third-Order Hamiltonian Operators”, J. Geom. Phys., 85 (2014), 16–28  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    19. Pavlov M.V., Vitolo R.F., “on the Bi-Hamiltonian Geometry of Wdvv Equations”, Lett. Math. Phys., 105:8 (2015), 1135–1163  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    20. Agafonov S.I., “Local Classification of Singular Hexagonal 3-Webs With Holomorphic Chern Connection Form and Infinitesimal Symmetries”, Geod. Dedic., 176:1 (2015), 87–115  crossref  mathscinet  zmath  isi  scopus  scopus
    21. Y. Kodama, B. G. Konopelchenko, “Confluence of hypergeometric functions and integrable hydrodynamic-type systems”, Theoret. and Math. Phys., 188:3 (2016), 1334–1357  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    22. Ferapontov E.V., Pavlov M.V., Vitolo R.F., “Towards the Classification of Homogeneous Third-Order Hamiltonian Operators: Table 1.”, Int. Math. Res. Notices, 2016, no. 22, 6829–6855  crossref  isi
    23. Agafonov S.I., “Note on Generic Singularities of Planar Flat 3-Webs”, Manuscr. Math., 154:1-2 (2017), 185–193  crossref  mathscinet  zmath  isi
    24. Dynnikov I.A. Glutsyuk A.A. Mironov A.E. Taimanov I.A. Vesnin A.Yu., “The Conference “Dynamics in Siberia”, Novosibirsk, February 26 - March 4, 2017”, Sib. Electron. Math. Rep., 14 (2017), A7–A30  mathnet  crossref  mathscinet  isi  scopus  scopus
    25. O. I. Mokhov, N. A. Strizhova, “Classification of the associativity equations possessing a Hamiltonian structure of Dubrovin–Novikov type”, Russian Math. Surveys, 73:1 (2018), 175–177  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    26. Pavlov V M., Stoilov N.M., “The Wdvv Associativity Equations as a High-Frequency Limit”, J. Nonlinear Sci., 28:5 (2018), 1843–1864  crossref  mathscinet  isi  scopus
    27. O. I. Mokhov, N. A. Pavlenko, “Classification of the associativity equations with a first-order Hamiltonian operator”, Theoret. and Math. Phys., 197:1 (2018), 1501–1513  mathnet  crossref  crossref  adsnasa  isi  elib
    28. Prykarpatski A.K., “On the Solutions to the Witten-Dijkgraaf-Verlinde-Verlinde Associativity Equations and Their Algebraic Properties”, J. Geom. Phys., 134 (2018), 77–83  crossref  mathscinet  zmath  isi  scopus
    29. O. I. Mokhov, N. A. Strizhova, “Integriruemost po Liuvillyu reduktsii uravnenii assotsiativnosti na mnozhestvo statsionarnykh tochek integrala v sluchae trekh primarnykh polei”, UMN, 74:2(446) (2019), 191–192  mathnet  crossref  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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