05. Dezember 2023
Sebastian Ohrem (KIT)
Breather solutions to quasilinear wave equations
We consider the quasilinear wave equation
V(x) utt - uxx+ Γ(x) (ut3)t =0 on R x R
which arises in the study of localized electromagnetic waves modeled by Maxwell equations with Kerr-type optical materials. We are interested in time-periodic, spatially localized solutions, called breathers.
For a compactly supported nonlinear potential Γ and several choices of the linear potential V, we prove existence of breathers using variational methods, and discuss their regularity.
We also consider quasilinear wave equations corresponding to materials of cylindrical geometry or materials with temporally delayed nonlinear response.
This is joint work with Wolfgang Reichel (KIT).