Abstract
This paper studies the exact boundary controllability of the semi-linear Schrödinger equation posed on a bounded domain Ω ⊂ R n with either the Dirichlet boundary conditions or the Neumann boundary conditions. It is shown that if s > n 2 , or 0 ⩽ s < n 2 with 1 ⩽ n < 2 + 2 s , or s = 0 , 1 with n = 2 , then the systems are locally exactly controllable in the classical Sobolev space H s ( Ω ) around any smooth solution of the cubic Schrödinger equation.
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