π kinks in a parametrically driven sine-Gordon chain

We consider the sine-Gordon chain driven by a high-frequency parametric force in the presence of loss. Using an analytical approach based on the method of averaging in fast oscillations, we predict that such a parametric force may support propagation of π kinks, which are unstable in the standard sine-Gordon model. The steady-state velocity of the π kinks is calculated, and the analytical results are in good agreement with direct numerical simulations.