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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 171, Number 2, Pages 208–224
DOI: https://doi.org/10.4213/tmf8365 (Mi tmf8365) 		 
This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (568 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf8365
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.
Received: 17.05.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 171, Issue 2, Pages 600–615
DOI: https://doi.org/10.1007/s11232-012-0058-x
Bibliographic databases:
Document Type: Article
Language: Russian
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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  • https://www.mathnet.ru/eng/tmf/v171/i2/p208
    • This publication is cited in the following 6 articles:
    1. Ghezelbash A.M., “M-Branes on Minimal Surfaces”, Eur. Phys. J. Plus, 137:2 (2022), 196  crossref  isi
    2. Vasicek J. Vitolo R., “Wdvv Equations and Invariant Bi-Hamiltonian Formalism”, J. High Energy Phys., 2021, no. 8, 129  crossref  mathscinet  isi
    3. 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
    4. 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
    5. 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
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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