Geodesic
Integrable structures for a~generalized Monge--Amp\`ere equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 2, pp. 208-224

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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, WDVV equation, two-dimensional topological field theory.
Mots-clés : jet space 
@article{TMF_2012_171_2_a2,
     author = {A. M. Verbovetsky and R. Vitolo and P. Kersten and I. S. Krasil'shchik},
     title = {Integrable structures for a~generalized {Monge--Amp\`ere} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {208--224},
     publisher = {mathdoc},
     volume = {171},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a2/}
}
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A. M. Verbovetsky; R. Vitolo; P. Kersten; I. S. Krasil'shchik. Integrable structures for a~generalized Monge--Amp\`ere equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 171 (2012) no. 2, pp. 208-224. http://geodesic.mathdoc.fr/item/TMF_2012_171_2_a2/