Sebastian Ohrem

activity

20222025

collaborators

5 papers

math.AP2025

Breather solutions to nonlinear Maxwell equations with retarded material laws

Sebastian Ohrem

We consider Maxwell's equations for Kerr-type optical materials, which are magnetically inactive and have a nonlinear response to electric fields. This response consists of a linea…

math.AP2025

Breather solutions for semilinear wave equations

Julia Henninger, Sebastian Ohrem, Wolfgang Reichel

We prove existence of real-valued, time-periodic and spatially localized solutions (breathers) of semilinear wave equations $V (x) u_{tt} - u_{xx} = Γ (x) ∣ u ∣^{p - 1} u$ on $\mathbb{R}^…

math.AP2025

Travelling breather solutions in waveguides for cubic nonlinear Maxwell equations with retarded material laws

Sebastian Ohrem, Wolfgang Reichel

For Maxwell's equations with nonlinear polarization we prove the existence of time-periodic breather solutions travelling along slab or cylindrical waveguides. The solutions are TE…

math.AP2024

Existence of traveling breather solutions to cubic nonlinear Maxwell equations in waveguide geometries

Sebastian Ohrem, Wolfgang Reichel

We consider the full set of Maxwell equations in a slab or cylindrical waveguide with a cubically nonlinear material law for the polarization of the electric field. The nonlinear p…

math.AP2022

Wellposedness for a (1+1)-dimensional wave equation with quasilinear boundary condition

Sebastian Ohrem, Wolfgang Reichel, Roland Schnaubelt

We consider the linear wave equation $V (x) u_{tt} (x, t) - u_{xx} (x, t) = 0$ on $[0, \infty) \times [0, \infty)$ with initial conditions and a nonlinear Neumann boundary condition $u_…