1. Februar 2022
Wolfgang Reichel (KIT)
Spatially localized time-periodic solutions of semilinear wave equations
We consider semilinear wave equations on the real line, on R^n, on bounded intervals, or on a particular quantum graph. By a variational method we establish the existence of spatially localized, time-periodic solutions. The method relies on a careful design of the set-up and the time period to allow for spectral gaps in the linear wave operator (when restricted to a domain of spatially localized, time-periodic functions). The spectral gaps are constructed and analyzed by ODE methods. The talk is based on collaborations with Julia Henninger, Andreas Hirsch, Simon Kohler , and Daniela Maier (Karlsruhe Institute of Technology).