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September  2012, 2(3): 247-270. doi: 10.3934/mcrf.2012.2.247

## Controllability of the cubic Schroedinger equation via a low-dimensional source term

 1 DiMaD, Università di Firenze, via delle Pandette 9, Firenze, 50127, Italy

Received  May 2011 Revised  November 2011 Published  August 2012

We study controllability of $d$-dimensional defocusing cubic Schroe-din-ger equation under periodic boundary conditions. The control is applied additively, via a source term, which is a linear combination of few complex exponentials (modes) with time-variant coefficients - controls. We manage to prove that controlling $2^d$ modes one can achieve controllability of the equation in each finite-dimensional projection of the evolution space $H^{s}(\mathbb{T}^d), \ s>d/2$, as well as approximate controllability in $H^{s}(\mathbb{T}^d)$. We also present a negative result regarding exact controllability of cubic Schroedinger equation via a finite-dimensional source term.
Citation: Andrey Sarychev. Controllability of the cubic Schroedinger equation via a low-dimensional source term. Mathematical Control & Related Fields, 2012, 2 (3) : 247-270. doi: 10.3934/mcrf.2012.2.247
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##### References:
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