Controllability of NLS in the vicinity of solitary wave solutions

Details Controllability of NLS in the vicinity of solitary wave solutions Controllability of NLS in the vicinity of solitary wave solutions

2006-08-05

arxiv.org/abs/math/0608135v1

Mathematics

Optimization and Control

27 pages

Scientific paper

Local exact controllability of the 1D 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 J.-L. 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.

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