Mapping Between Nonlinear Schödinger Equations with Real and Complex Potentials

Abstract

A mapping between stationary solutions of nonlinear Schödinger 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 the damped dynamics of a quantum harmonic oscillator and the case of dissipative periodic soliton solutions of the nonlinear Schrödinger equation with complex potential.