A mapping between the stationary solutions of nonlinear Schrödinger equations with real and complex potentials is constructed and a set of exact solutions with real energies are obtained for a large class of complex potentials. As specific examples we consider the case of dissipative periodic soliton solutions of the nonlinear Schrödinger equation with complex potential.
Mario Salerno. "Mapping Between Nonlinear Schrödinger Equations with Real and Complex Potentials." J. Geom. Symmetry Phys. 32 25 - 35, 2013. https://doi.org/10.7546/jgsp-32-2013-25-35