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
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35Q60 Equations of electromagnetic theory and optics
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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