# Local Exact Controllability of a One-Dimensional Nonlinear Schrödinger Equation

Abstract : We consider a one-dimensional nonlinear Schrödinger 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. Read More: http://epubs.siam.org/doi/10.1137/140951618
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Journal articles

https://hal.archives-ouvertes.fr/hal-01377135
Contributor : Marie-Annick Guillemer <>
Submitted on : Thursday, October 6, 2016 - 2:36:48 PM
Last modification on : Friday, November 16, 2018 - 1:35:34 AM

### Citation

Karine Beauchard, Horst Lange, Holger Teismann. Local Exact Controllability of a One-Dimensional Nonlinear Schrödinger Equation. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2016, 53 (5), pp.2781 - 2818. ⟨10.1137/140951618⟩. ⟨hal-01377135⟩

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