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- W2941484859 abstract "We prove that the generalized phase space of KdV on S 1 , i.e. (L 0 2 ([0,1]),ω G ) where ω G denotes the Gardner symplectic structure on the space L 0 2 ([0,1]), of L 2 functions with average 0, is symplectomorphic to the phase space (l 1/2 2 (ℝ 2 ),ω 0 ) of infinitely many harmonic oscillators, where l 1/2 2 (ℝ 2 ) denotes the Hilbert space of sequences (x n ,y n ) n≥1 satisfying ∑ n≥1 n(x n 2 +y n 2 )<∞ endowed with the canonical symplectic structure ω 0 . The symplectomorphism Ω from (L 0 2 ([0,1],ω G ) onto (l 1/2 2 (ℝ 2 ),ω 0 ) is shown to be bianalytic. Similar results hold for the periodic Toda equations and the periodic nonlinear Schrodinger equation (defocusing)." @default.
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- W2941484859 date "1993-01-01" @default.
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- W2941484859 title "The symplectic structure of the phase space for the periodic Korteweg-de Vries equation" @default.
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