Singularity formation for the nonlinear Schrodinger equation |
Abstract: I will consider the focusing nonlinear Schrodinger equation iu_t+\Delta u+u|u|^{p-1}=0. This equation is a universal model for the propagation of waves in a nonlinear medium. From the mathematical point of view, it is an infinite dimensional Hamiltonian system with infinite speed of propagation. Of particular interest is the existence of finite time blow up solutions which is known since the 60's, but the existence argument is purely obstructive and does not give any insight into the detailed description of the singularity formation. I will give an overview of the state of the art on this problem. In particular, I will present a series of recent results obtained in collaboration with Frank Merle which allow in some cases an explicit description of the singularity formation. |
Web page: Alexandru I. Suciu | Comments to: alexsuciu@neu.edu | |
Posted: September 28, 2006 | URL: http://www.math.neu.edu/bhmn/raphael06.html |