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.
KIT 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 (Liao , 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 )
