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.
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Kivshar et al. (1992) studied this question.
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