Instabilities, solitons, and rogue waves in PT-coupled nonlinear waveguides

We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time (PT)-symmetric system of linearly-coupled nonlinear Schr\"odinger equations, which describes a Kerr-nonlinear optical coupler with mutually balanced gain and loss in its cores. Besides the linear coupling, the overlapping cores are coupled through cross-phase-modulation term too. While the rogue waves, built according to the pattern of the Peregrine soliton, are (quite naturally) unstable, we demonstrate that the focusing cross-phase-modulation interaction results in their partial stabilization. For PT-symmetric and antisymmetric bright solitons, the stability region is found too, in an exact analytical form, and verified by means of direct simulations.