Project Area A • Mathematical Foundations

Mathematical foundations deals with general and fundamental questions concerning the analysis and numerics of wave phenomena, often by analyzing characteristic examples.

Projects

A1	Large signals in nonlinear fiber optics (Hundertmark, Kunstmann)
A2	Numerical methods for wave problems with nontrivial boundary conditions and nonlocal material laws (Hochbruck, Lubich)
A3	Adaptive implicit space-time discretization for wave equations (Dörfler, Wieners)
A4	Time integration of Maxwell and wave-type equations (Hochbruck, Schnaubelt)
A5	Qualitative behavior of nonlinear Maxwell equations (Schnaubelt)
A6	Localized solutions for nonlinear Maxwell and wave-type equations (Reichel)
A7	Numerical methods for highly oscillatory problems (Hochbruck, Jahnke, Lubich)
A8	Failure of amplitude equations (7/2015 - 6/2019)
A9	Spectral methods for dispersive equations (7/2015 - 6/2019)
A10	Standing and moving pulses in periodic media (7/2019 - 6/2023)
A11	Electromagnetic fields interacting with quantum matter (Anapolitanos, Hundertmark)
A12	Dynamics of the Gross–Pitaevskii equation and related dispersive equations (Schneider)
A13	Dispersive estimates for wave equations with low regularity coefficients (Frey, Schnaubelt)
A14	Nonlinear stability of periodic waves in dissipative-dispersive systems (Frey, de Rijk)
A15	Localized methods for the wave equation with strong heterogeneities in space and time (Maier)