By Magri's theorem, self-dual gravity is completely integrable.
Nutku, Yavuz
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only], Tome 3 (2007), / Harvested from The Electronic Library of Mathematics
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Publié le : 2007-01-01
EUDML-ID : urn:eudml:doc:54089 
@article{05241547,
     title = {By Magri's theorem, self-dual gravity is completely integrable.},
     journal = {SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]},
     volume = {3},
     year = {2007},
     zbl = {1136.83314},
     language = {en},
     url = {http://dml.mathdoc.fr/item/05241547}
}

Nutku, Yavuz. By Magri's theorem, self-dual gravity is completely integrable.. SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only], Tome 3 (2007) . http://gdmltest.u-ga.fr/item/05241547/