Dynamics and control of oscillations in a complex crystalline lattice

Feedback control for some solutions of the sine-Gordon equation

“…The biggest step of integration is assumed to be equal to 2 · 10 −3 . (5) and (8). One can note that the profiles in Figs.…”

“…Independence on the initial conditions may be provided by inclusion of a control with a feedback using algorithms (5) and (8).…”

“…One possibility to recover the unified shape of the wave may be in applications of the control methods [7][8][9]. Methods of control theory (cybernetics) attract a growing interest of physicists for more than two decades [9][10][11].…”

“…Previously these methods were mainly used for oscillation control problems for systems governed by ordinary differential equations [9,12]. Use of the control mechanism in the wave processes concern envelope wave equations [7,13], reaction-diffusion equations [14,15], and the sine-Gordon equation [8,16,17]. Some control related methods for sin-Gordon equation use feedforward (nonfeedback) controlling actions [7,13].…”

“…However, the feedback control methods look more promising. A successive attempt to extend the control methods to the wave problems has been done in [8,16] where the boundary conditions were controlled to achieve significant difference in the wave behavior of the sine-Gordon equation and some of its generalization.…”