Organizers of this minisymposium are
All non-trivial materials respond in a nonlinear way to electromagnetic fields. The corresponding mathematical model is given by nonlinear Maxwell equations. In the time dependent case these are quasilinear equations – often with time delay terms in the polarization. A time harmonic monochromatic ansatz leads to an elliptic system which can be considered for a fixed frequency or for a variable frequency as an operator pencil. Nonlinearities can appear also in the boundary conditions or in Ohm’s law. In many applications, e.g. for photonic crystals or surface plasmons, the material is inhomogeneous and includes interfaces of different homogeneous or periodic materials. Moreover, in the presence of metallic structures the linear problem is non-selfadjoint.
This minisymposium presents recent developments in the analysis of nonlinear Maxwell equations including well posedness for the instantaneous as well as the time delayed case; variational and bifurcation methods for the existence of monochromatic (time harmonic) or polychromatic solutions; and the study of the dynamics and asymptotics of wave packets.