THE STABILITY OF NONLINEAR SCHRODINGER EQUATIONS WITH A POTENTIAL IN HIGH SOBOLEV NORMS REVISITED

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We consider the nonlinear Schrodinger equations with a potential on T-d. For almost all potentials, we show the almost global stability in very high Sobolev norms. We apply an iteration of the Birkhoff normal form, as in the formulation introduced by Bourgain [4]. This result reproves a dynamical consequence of the infinite dimensional Birkhoff normal form theorem by Bambusi and Grebert [2]
Publisher
AMER INST MATHEMATICAL SCIENCES
Issue Date
2016-03
Language
English
Article Type
Article
Keywords

DIMENSIONAL HAMILTONIAN-SYSTEMS; PARTIAL-DIFFERENTIAL-EQUATIONS; BIRKHOFF NORMAL-FORM; GROWTH; DIFFUSION; BOUNDS

Citation

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.15, no.2, pp.341 - 365

ISSN
1534-0392
DOI
10.3934/cpaa.2016.15.341
URI
http://hdl.handle.net/10203/209044
Appears in Collection
MA-Journal Papers(저널논문)
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