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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.<\/jats:p>","DOI":"10.1137\/140951618","type":"journal-article","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T11:45:10Z","timestamp":1441712710000},"page":"2781-2818","source":"Crossref","is-referenced-by-count":10,"title":["Local Exact Controllability of a One-Dimensional Nonlinear Schr\u00f6dinger Equation"],"prefix":"10.1137","volume":"53","author":[{"given":"Karine","family":"Beauchard","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Horst","family":"Lange","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Holger","family":"Teismann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"key":"atypb1","unstructured":"M. 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