Large time asymptotics of solutions to the anharmonic oscillator model from nonlinear optics

Abstract

The anharmonic oscillator model describing the propagation of electromagnetic waves in an exterior domain containing a nonlinear dielectric medium is investigated. The system under consideration consists of a generally nonlinear second order differential equation for the dielectrical polarization coupled with Maxwell's equations for the electromagnetic field. Local decay of the electromagnetic field for t to infinity in the charge free case is shown for a large class of potentials. (This paper has been accepted for publication in the SIAM Journal on Mathematical Analysis.)