Well-posedness for the Schrödinger-Debye equation

Abstract

The Maxwell-Debye system describes the non resonant delayed interaction of an electromagnetic wave with a media. In these equations A denotes the envelope of a light wave that goes through a media which response is non resonant. This wave induces a change \nu of refractive index in the material (initially \eta_0 for an electromagnetic wave of frequency \omega_0) with a slight delay \tau. The magnitude and the sign of the nonlinear coupling of the matter with the wave is described by the parameter \eta_2. The light velocity in the vacuum is denoted by c and k denotes the wave.