Nonlinear localized modes in PT-symmetric Rosen-Morse potential wells

We report the existence and properties of localized modes described by a nonlinear Schrodinger equation with a complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one-dimensional and two-dimensional geometry with self-focusing and self-defocusing Kerr nonlinearity. Linear stability analysis reveals that these localized modes are unstable for all real values of the potential parameters, although the corresponding linear Schrodinger eigenvalue problem possesses unbroken PT symmetry. This result has been verified by the direct numerical simulation of the governing equation. The transverse power-flow density associated with these localized modes has also been examined. DOI: 10.1103/PhysRevA.87.045803