Feedback control of the sine–Gordon antikink

•Distributed control algorithm for the antikink stable propagation for the sine–Gordon equation.•Suppression of oscillations caused by non-consistent initial conditions.•Generation of antikink by the feedback control from arbitrary initial conditions.

A new distributed speed-gradient feedback control algorithm for the sine–Gordon (SG) equation is proposed. It creates the antikink traveling wave mode for a broader class initial conditions compared to the uncontrolled system. In real physical problems it is difficult to provide consistent initial conditions for the second-order (in time) equations. Therefore for an uncontrolled system even small variations in the initial velocity relative to that of the exact antikink solution of the SG equation give rise to growing oscillations. The control algorithm allows one both to suppress defects and to obtain stable propagation of an antikink in the form of the exact traveling wave solution of the SG equation. In contrast to the existing algorithms the proposed algorithm does not require additional dissipative term for wave generation.