Geodesic
Poisson brackets for two-dimensional systems that can be~integrated by~the inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 1, pp. 34-40

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The method of time asymptotics is used to calculate the Poisson brackets of the scattering data for the auxiliary spectral problem associated with the II Davey–Stewartson system of equations; trace identities are obtained. Explicit expressions for action–angle variables are given. 
@article{TMF_1990_83_1_a3,
     author = {V. G. Bakurov},
     title = {Poisson brackets for two-dimensional systems that can be~integrated by~the inverse scattering method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {34--40},
     publisher = {mathdoc},
     volume = {83},
     number = {1},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a3/}
}
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V. G. Bakurov. Poisson brackets for two-dimensional systems that can be~integrated by~the inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 83 (1990) no. 1, pp. 34-40. http://geodesic.mathdoc.fr/item/TMF_1990_83_1_a3/