Geodesic
On third Poisson structure of KdV equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 3, pp. 461-466

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The third Poisson structure of KdV equation in terms of canonical “free fields” and reduced WZNW model is discussed. We prove that it is “diagonalized” in the Lagrange variables which were used before in formulation of $2d$ gravity. We propose a quantum path integral for KdV equation based on this representation. 
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     author = {A. S. Gorsky and A. V. Marshakov and A. Yu. Orlov and V. N. Rubtsov},
     title = {On third {Poisson} structure of {KdV} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {103},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_103_3_a7/}
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A. S. Gorsky; A. V. Marshakov; A. Yu. Orlov; V. N. Rubtsov. On third Poisson structure of KdV equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 103 (1995) no. 3, pp. 461-466. http://geodesic.mathdoc.fr/item/TMF_1995_103_3_a7/