| Date: | Tue, 29 Apr 2008 |
| From: | Leonid Chindelevitch |
| Subject: | SPAMS Thursday, 5 PM, in 4-231 |
Hello everyone,
This week's SPAMS talk will deal with the fascinating topic of solitons. Vedran
Sohinger will enlighten us at the usual time and place. Please note that Ilya
Nikokoshev will be speaking the following week. Hope to see you all then!
Leonid, Denis and Michael,
SPAMS organizers.
Title: Soliton Solutions to the Nonlinear Schrodinger Equation
In this talk, I will consider solitary wave solutions to the Nonlinear
Schrodinger Equation which oscillate in time, but have a fixed profile in
space. The main result that will be presented concerns the existence of such
solutions under appropriate assumptions on the nonlinearity. We will observe
that the solitary wave solutions correspond to functions which give us the
optimal constant in the Gagliardo-Nirenberg Inequality. If time permits, I will
discuss the notion of soliton stability. The results that I plan to present come
from the work of Michael Weinstein in the 1980s.