Beauchard, Karine, Lange, Horst and Teismann, Holger (2015). LOCAL EXACT CONTROLLABILITY OF A ONE-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION. SIAM J. Control Optim., 53 (5). S. 2781 - 2819. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7138

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Abstract

We consider a one-dimensional nonlinear Schrodinger equation, modeling a Bose-Einstein condensate in an infinite square-well potential (box). This is a nonlinear control system in which the state is the wave function of the Bose-Einstein condensate and the control is the length of the box. We prove that local exact controllability around the ground state (associated with a fixed length of the box) holds generically with respect to the chemical potential mu, i.e., up to an at most countable set of mu-values. The proof relies on the linearization principle and the inverse mapping theorem, as well as ideas from analytic perturbation theory.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Beauchard, KarineUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Lange, HorstUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
Teismann, HolgerUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-415611
DOI: 10.1137/140951618
Journal or Publication Title: SIAM J. Control Optim.
Volume: 53
Number: 5
Page Range: S. 2781 - 2819
Date: 2015
Publisher: SIAM PUBLICATIONS
Place of Publication: PHILADELPHIA
ISSN: 1095-7138
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
BILINEAR OPTIMAL-CONTROL; QUANTUM PARTICLE; AXIAL LOAD; SHORTCUTSMultiple languages
Automation & Control Systems; Mathematics, AppliedMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/41561

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