Solitons in a nonlinear Schrödinger equation withPT-symmetric potentials and inhomogeneous nonlinearity: Stability and excitation of nonlinear modes

We report branches of explicit expressions for nonlinear modes in parity-time (PT) -symmetric potentials of several types. For the single-well and double-well potentials the found solutions are two-parametric and appear to be stable even when the PT symmetry of respective underlying linear models is broken. Based on the examples of these solutions we describe an algorithm of excitation of a stable nonlinear mode in a model whose linear limit is unstable. The method is based on the adiabatic change of the control parameter driving the mode along a branch bifurcating from a stable linear mode. The suggested algorithm is confirmed by extensive numerical simulations.