4. Dezember 2019
Giulio Romani (Uni Halle)
Bifurcations and nonlinear eigenvalues in Maxwell's equations
Abstract:
In this talk I will present some recent results about bifurcation of small solutions for the time-harmonic Maxwell's equation in R^3 in presence of straight interfaces between layers of different materials (dielectrics and/or metals). A suitable ansatz leads us to a nonlinear Schrödinger equation which depends nonlinearly also on the frequency, here considered as a spectral parameter. For some configurations of the materials we find an eigenpair and from it we are able to prove the existence of a branch of small solutions and to provide their asymptotic expansion. These results are part of an ongoing project in collaboration with Tomáš Dohnal (MLU Halle).