Stabilization of breathers in a parametrically driven sine-Gordon system with loss

We demonstrate that in a parametrically driven sine-Gordon system with loss, a breather, if driven, can be maintained in a steady state at half the external frequency. In the small-amplitude limit the system is described by the effective perturbed nonlinear Schrödinger equation. For an arbitrary breather amplitude the threshold field is determined by a perturbation method and compared with direct numerical simulations. Excellent agreement is found.