Controllability of the cubic Schroedinger equation via a low-dimensional source term
نویسنده
چکیده
We study controllability of 2D defocusing cubic Schroedinger equation under periodic boundary conditions and control applied via source term (additively). The source term is a linear combination of few complex exponentials (modes) with time-variant coefficients controls. We manage to prove that controlling just 4 modes one can achieve controllability of this equation in any finite-dimensional projection of its evolution space H(T), as well as approximate controllability in H(T), σ > 0. We also present negative result regarding exact controllability of cubic Schroedinger equation via a finite-dimensional source term.
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