Modulation theory in PT-symmetric magnetic metamaterial arrays in the continuum limit

We present results on the dynamics of split-ring dimers having both gain and loss in one-dimensional nonlinear parity-time- (PT-)symmetric magnetic metamaterials. For the long-wave (continuum) limit approximation and in the weakly nonlinear limit, we show analytic results on the existence of gap soliton solutions and on symmetry-breaking phenomenon at a critical value of the gain or loss term.