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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.