Nonlocal Schrodinger-Maxwell-Bloch Equations

Abstract

In this paper we research the (1+1)-dimensional system of Schr¨odinger-MaxwellBloch equations (NLS-MBE), which describes the optical pulse propagation in an erbium doped fiber and find PT-symmetric and reverse space-time Schr¨odinger-Maxwell-Bloch equations, i.e. the kinds of nonlocal Schr¨odinger-Maxwell-Bloch equations. In particular case, the system of Schr¨odinger-Maxwell-Bloch equations is integrable by the Inverse Scattering Method as shown in the work of M.Ablowitz and Z.Musslimani. Following this method we prove the integrability of the nonlocal system of Schr¨odinger-Maxwell-Bloch equations by Lax pairs. Also the explicit and different seed solutions are constructed by using Darboux transformation.