|Date:||Mon, April 4, 2011|
|Place:||Research II Lecture Hall|
Abstract: The nonlinear Schrödinger equation is an asymptotic equation for wave propagation for many problems, including water waves, nonlinear optics and optical fibers.
Energy conservation and elementary arguments imply wellposedness, but the estimates connected with the contraction argument give little information for large time and/or large initial data beyond mere boundedness.
I will review examples of solutions and explain that and why the propagation of energy in phase space is fairly robust.