Nonlinear modes in the harmonic PT-symmetric potential

We study the families of nonlinear modes described by the nonlinear Schrodinger equation with the PT-symmetric harmonic potential x(2) - 2i alpha x. The nonlinear modes found display a number of interesting features. In particular, we have observed that modes bifurcating from different eigenstates of the underlying linear problem can actually belong to the same family of nonlinear modes. We also show that by proper adjustment of the coefficient a it is possible to enhance the stability of small-amplitude and strongly nonlinear modes compared to the well-studied case of the real harmonic potential.