Controllability of the nonlinear Schrödinger equation in the vicinity of the ground state

Abstract

Abstract Local exact controllability of the one‐dimensional NLS (subject to zero‐boundary conditions) with distributed control is shown to hold in a H 1 ‐neighbourhood of the nonlinear ground state. The Hilbert Uniqueness Method ( HUM ), due to Lions, is applied to the linear control problem that arises by linearization around the ground state. The application of HUM crucially depends on the spectral properties of the linearized NLS operator which are given in detail. Copyright © 2007 John Wiley & Sons, Ltd.