Monotonic control of nonlinear oscillations and waves of ensemble of pendulums

Some parametric regimes of control of nonlinear oscillations and waves, described by the sine-Gordon equation with dissipation and time-dependant external field f(t) are considered. Special transformations of time-space variables convert this equation to a new form with an effective coefficient of “dissipation” depending on f(t). Three regimes of parametric control are investigated, when f(t) is a monotone function of time. The first when f(t) is exponential function means that the external field compensates the dissipation energy completely and the effective (but not real) coefficient becomes zero. The other two lead to amplifying of oscillations or sharp damping. In the first case some new exact solutions of the sine-Gordon equation are analyzed