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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 {pi} kinks, which are unstable in the standard sine-Gordon model. The steady-state velocity of the {pi} kinks is calculated, and the analytical results are in good agreement with direct numerical simulations.

π kinks in a parametrically driven sine-Gordon chain