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. (C) 2016 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)147-155
Number of pages9
JournalWave Motion
Volume65
DOIs
StatePublished - Sep 2016

    Research areas

  • Nonlinear wave, Feedback control, Nonlinear equation, Numerical solution, EQUATION, STABILIZATION, WAVES, MODEL

ID: 13719916