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We study numerically a parametrically driven discrete nonlinear Schr\"odingerequation modelling periodically curved waveguide arrays. We show that discretesurface solitons persist, but their threshold power is altered by the drive.There are critical drives at which the threshold values vanish. We also showthat parametric drives can create resonance with a phonon making a new barrierfor discrete solitons. By calculating the corresponding Floquet multipliers, wefind that the stability of symmetric and antisymmetric off-side discretesurface solitons switches approximately at the critical drives forthresholdless solitons.

Thresholdless discrete surface solitons and stability switchings in periodically curved waveguides