  We investigate the existence of stable soliton solution in a system described
by complex Ginzburg-Landau (CGL) equation with near parity reflection - time
reversal ($\mathcal{PT}$) symmetric Rosen-Morse potential. In this study, the
stability of solution is examined by numerical analysis to show that solitons
are stable for some parameter ranges. The dynamical properties such as
evolution and transverse energy flow for both self-focusing and self-defocusing
nonlinear mode are also analyzed. The obtained results are useful for
experimental designs and applications in related fields.
