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Indexed by:Journal Papers

Date of Publication:2016-01-01

Journal:MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY

Included Journals:SCIE

Volume:239

Issue:1134

Page Number:1-+

ISSN No.:0065-9266

Key Words:KAM tori; Normal form; Stability; p-tame property; KAM technique

Abstract:We prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrodinger equation
   root-1u(t) = u(xx) - M(xi)u + epsilon vertical bar u vertical bar(2)u,
   subject to Dirichlet boundary conditions u(t, 0) = u(t, pi) = 0, where M-xi is a real Fourier multiplier. More precisely, we show that, for a typical Fourier multiplier M-xi, any solution with the initial datum in the delta-neighborhood of a KAM torus still stays in the 2 delta-neighborhood of the KAM torus for a polynomial long time such as vertical bar t vertical bar = delta(-M) for any given M with 0 <= M <= C(epsilon), where C(epsilon) is a constant depending on e and C(epsilon) -> infinity as epsilon -> 0.