Geodesic
$2+1$~Toda chain. I.~Inverse scattering method
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 3, pp. 323-339

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A formal scheme of the inverse scattering method is constructed for the $2+1$ Toda chain in the class of rapidly decreasing Cauchy data. 
@article{TMF_1988_75_3_a0,
     author = {V. D. Lipovskii and A. V. Shirokov},
     title = {$2+1${~Toda} chain. {I.~Inverse} scattering method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {323--339},
     publisher = {mathdoc},
     volume = {75},
     number = {3},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_3_a0/}
}
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V. D. Lipovskii; A. V. Shirokov. $2+1$~Toda chain. I.~Inverse scattering method. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 3, pp. 323-339. http://geodesic.mathdoc.fr/item/TMF_1988_75_3_a0/