  We consider a one-dimensional Bose-Einstein condensate in a infinite
square-well (box) potential. 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.
