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.

Festschrift in honor of the 65th birthday of Professor Vladimir Gerdjikov submitted to Journal of Geometry and Symmetry in Physics (14 pages, 2 figures)