Mapping Between Nonlinear Sch\"odinger Equations with Real and Complex Potentials
Pattern Formation and Solitons
2026-04-03 v2 Quantum Gases
Abstract
A mapping between stationary solutions of nonlinear Sch\"odinger 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 Schr\"odinger equation with complex potential.
Cite
@article{arxiv.1306.3643,
title = {Mapping Between Nonlinear Sch\"odinger Equations with Real and Complex Potentials},
author = {Mario Salerno},
journal= {arXiv preprint arXiv:1306.3643},
year = {2026}
}
Comments
Festschrift in honor of the 65th birthday of Professor Vladimir Gerdjikov submitted to Journal of Geometry and Symmetry in Physics (14 pages, 2 figures)