Geodesic
A KAM theorem for space-multidimensional Hamiltonian PDEs
Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 142-162

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We present an abstract KAM theorem adapted to space-multidimensional Hamiltonian PDEs with smoothing nonlinearities. The main novelties of this theorem are the following: (i) the integrable part of the Hamiltonian may contain a hyperbolic part and, as a consequence, the constructed invariant tori may be unstable; (ii) it applies to singular perturbation problems. In this paper we state the KAM theorem and comment on it, give the main ingredients of the proof, and present three applications of the theorem. 
@article{TRSPY_2016_295_a6,
     author = {L. H. Eliasson and B. Gr\'ebert and S. B. Kuksin},
     title = {A {KAM} theorem for space-multidimensional {Hamiltonian} {PDEs}},
     journal = {Informatics and Automation},
     pages = {142--162},
     publisher = {mathdoc},
     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a6/}
}
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L. H. Eliasson; B. Grébert; S. B. Kuksin. A KAM theorem for space-multidimensional Hamiltonian PDEs. Informatics and Automation, Modern problems of mechanics, Tome 295 (2016), pp. 142-162. http://geodesic.mathdoc.fr/item/TRSPY_2016_295_a6/