- Series
- PDE Seminar
- Time
- Tuesday, February 21, 2023 - 3:00pm for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jonas Lührmann – Texas A&M University – luhrmann@math.tamu.edu – http://people.tamu.edu/~luhrmann/
- Organizer
- Gong Chen
Solitons are particle-like solutions to dispersive evolution equations
whose shapes persist as time goes by. In some situations, these solitons
appear due to the balance between nonlinear effects and dispersion, in
other situations their existence is related to topological properties of
the model. Broadly speaking, they form the building blocks for the
long-time dynamics of dispersive equations.
In this talk I will present joint work with W. Schlag on long-time decay
estimates for co-dimension one type perturbations of the soliton for the
1D focusing cubic Klein-Gordon equation (up to exponential time scales),
and I will discuss our previous work on the asymptotic stability of the
sine-Gordon kink under odd perturbations. While these two problems are
quite similar at first sight, we will see that they differ by a subtle
cancellation property, which has significant consequences for the
long-time dynamics of the perturbations of the respective solitons.