  We investigate the dynamical behavior of continuous and discrete Schrodinger
systems exhibiting parity-time (PT) invariant nonlinearities. We show that such
equations behave in a fundamentally different fashion than their nonlinear
Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger
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.
