Stability of periodic waves for 1D NLS

PDE Seminar
Tuesday, March 31, 2015 - 3:05pm
1 hour (actually 50 minutes)
Skiles 006
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.