Nonlinear Maxwell Equations

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. The time independet case (for time harmonic ansatzes) leads to an elliptic system which can be considered for a fixed frequency or for a variable frequency as a eigenvalue problem which is typically nonlinear also in the frequency parameter. In many applications, e.g. for surface plasmons or photonic crystals, the material is inhomogenous and includes interfaces of different homogenous or periodic materials. This complicates the analysis due to the presence of variable coefficients.

This minisymposium brings together scientists working on nonlinear Maxwell equations regarding analytical topics like well posedness of time dependent problems, existence of ground states, bound states and of eigenvalues in the time harmonic case, bifurcations of solutions, dynamics of waves or amplitude approximations of wave packets as well as numerical topics like finite element or discontinuous Galerkin approximations.