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

2011/05/09 by Andrey Sarychev, Sarychev, Andrey · 2 citations
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1105.1728

Abstract

We study controllability of d-dimensional defocusing cubic Schroedinger\nequation under periodic boundary conditions. The control is applied additively,\nvia a source term, which is a linear combination of few complex exponentials\n(modes) with time-variant coefficients - controls. We manage to prove that\ncontrolling at most 2^d modes one can achieve controllability of the equation\nin any finite-dimensional projection of the evolution space\nH^s( mathbbT^d), s>d/2, as well as approximate controllability in\nH^s( mathbbT^d). We also present negative result regarding exact\ncontrollability of cubic Schroedinger equation via a finite-dimensional source\nterm.\n

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