Feedback control of chaotic motions and unstable wave packets in a space-time-dependent system

By using feedback control in k space and pinning in x space we successfully stabilize unstable steady wave-packet solutions in a representation of the driven/damped nonlinear drift-wave system. Three typical solutions are chosen to be controlled. Without controlling they display different dynamical features: one is chaotic in time while coherent in space, another is chaotic both in time and in space, the third one is explosively unstable. All the states can be stabilized to the respective unstable regular reference states by our controlling schemes.