Rigorous numerics for NLS: bound states, spectra, and controllability

Abstract

In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof [6] of the local exact controllability of NLS.

30 pages, 2 figures