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JOURNALS // Teoreticheskaya i Matematicheskaya Fizika // Archive

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

This article is cited 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

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

DOI: 10.4213/tmf8365


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

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