Large time asymptotics of solutions to the anharmonic oscillator modelfrom nonlinear optics
Source file as Postscript Document

Frank Jochmann

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC 2000

35Q60 Equations of electromagnetic theory and optics
78A35 Motion of charged particles
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.)

Keywords: nonlinear optics, Maxwell's equations,exterior boundary value problem, asymptotic behaviour