The linear KdV-Schrödinger equation on the torus is small-time globally approximately controllable in L2 via imaginary bilinear controls on finite Fourier modes between equal-norm states, independently of the Schrödinger part.
Linear stability and instability of ion-acoustic plasma solitary waves
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Bilinear controllability for the linear KdV-Schr{\"o}dinger equation
The linear KdV-Schrödinger equation on the torus is small-time globally approximately controllable in L2 via imaginary bilinear controls on finite Fourier modes between equal-norm states, independently of the Schrödinger part.