We investigate the dynamical behavior of continuous and discrete Schr\”odinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schr\”odinger counterparts. In particular, the PT-symmetric nonlinear Schr\”odinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a two-element discretized version of this PT nonlinear Schr\”odinger equation. By obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry breaking conditions. This arrangement is unique in the sense that the exceptional points are fully dictated by the nonlinearity itself.

http://arxiv.org/abs/1310.7399
Pattern Formation and Solitons (nlin.PS)