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TMF, 2012, Volume 171, Number 2, Pages 208–224 (Mi tmf8365)  

This article is cited in 4 scientific papers (total in 4 papers)

Integrable structures for a generalized Monge–Ampère equation

A. M. Verbovetskya, R. Vitolob, P. Kerstenc, I. S. Krasil'shchika

a Independent University of Moscow, Moscow, Russia
b Department of Mathematics "E. De Giorgi", University of Salento, Lecce, Italy
c Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, Enschede, The Netherlands

Abstract: We consider a third-order generalized Monge–Ampère equation $u_{yyy}- u_{xxy}^2+u_{xxx}u_{xyy}=0$, which is closely related to the associativity equation in two-dimensional topological field theory. We describe all integrable structures related to it: Hamiltonian, symplectic, and also recursion operators. We construct infinite hierarchies of symmetries and conservation laws.

Keywords: Monge–Ampère equation, integrability, Hamiltonian operator, symplectic structure, symmetry, conservation law, jet space, WDVV equation, two-dimensional topological field theory

DOI: https://doi.org/10.4213/tmf8365

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English version:
Theoretical and Mathematical Physics, 2012, 171:2, 600–615

Bibliographic databases:

Received: 17.05.2012

Citation: A. M. Verbovetsky, R. Vitolo, P. Kersten, I. S. Krasil'shchik, “Integrable structures for a generalized Monge–Ampère equation”, TMF, 171:2 (2012), 208–224; Theoret. and Math. Phys., 171:2 (2012), 600–615

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Pavlov, R. F. Vitolo, “On the bi-Hamiltonian geometry of WDVV equations”, Lett. Math. Phys., 105:8 (2015), 1135–1163  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. M. V. Pavlov, R. F. Vitolo, “Remarks on the Lagrangian representation of bi-Hamiltonian equations”, J. Geom. Phys., 113 (2017), 239–249  crossref  mathscinet  zmath  isi  scopus
    3. A. M. Ghezelbash, V. Kumar, “Exact helicoidal and catenoidal solutions in five- and higher-dimensional Einstein-Maxwell theory”, Phys. Rev. D, 95:12 (2017), 124045  crossref  mathscinet  isi  scopus
    4. E. V. Ferapontov, M. V. Pavlov, R. F. Vitolo, “Systems of conservation laws with third-order Hamiltonian structures”, Lett. Math. Phys., 108:6 (2018), 1525–1550  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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