On action-angle variables for the second Poisson bracket of KdV

Kappeler, T; Makarov, M (2000). On action-angle variables for the second Poisson bracket of KdV. Communications in Mathematical Physics, 214(3):651-677.

Abstract

We prove that on the Sobolev spaces Hᴺ (S ¹) (N≥ 0), each leaf of the foliation, induced by the second Poisson bracket of KdV, admits global action-angle variables. The actions with respect to the first bracket raise to the actions with respect to the second bracket. The angles for the first bracket are, at the same time, angles for the second bracket.

Abstract

We prove that on the Sobolev spaces Hᴺ (S ¹) (N≥ 0), each leaf of the foliation, induced by the second Poisson bracket of KdV, admits global action-angle variables. The actions with respect to the first bracket raise to the actions with respect to the second bracket. The angles for the first bracket are, at the same time, angles for the second bracket.

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