Dynamics of Partial Differential Equations

Volume 4 (2007)

Number 2

Stability of spectral eigenspaces in nonlinear Schrödingerequations

Pages: 129 – 141

DOI: http://dx.doi.org/10.4310/DPDE.2007.v4.n2.a2

Authors

Dario Bambusi (Dipartimento di Matematica, Università degli studi di Milano, Italy)

Andrea Sacchetti (Dipartimento di Matematica Pura ed Applicata, Università degli studi di Modena, Italy)

Abstract

We consider the time-dependent non linear Schrödinger equations with a double well potential. We prove, in the semiclassical limit, that the finite dimensional eigenspace associated to the lowest two eigenvalues of the linear operator is almost invariant for any time.

Keywords

nonlinear Schrödinger equations; almost invariant manifolds

2010 Mathematics Subject Classification

35Bxx, 35K55, 35Q40

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