### Stability of periodic waves for 1D NLS

- Series
- PDE Seminar
- Time
- Tuesday, March 31, 2015 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Stephen Gustafson – UBC

Cubic focusing and defocusing Nonlinear Schroedinger Equations admit
spatially (and temporally) periodic standing wave solutions given
explicitly by elliptic functions. A natural question to ask is: are they
stable in some sense (spectrally/linearly, orbitally,
asymptotically,...), against some class of perturbations (same-period,
multiple-period, general...)? Recent efforts have slightly enlarged our
understanding of such issues. I'll give a short survey, and describe an
elementary proof of the linear stability of some of these waves. Partly
joint work in progress with S. Le Coz and T.-P. Tsai.