University of Toronto
                  PDE/Applied Math/Analysis Seminar
                    Friday 9 March 2007, 12:10-1:00pm
                          2195 Bahen Center      



SPEAKER:  Maciej Zworski

TITLE:    Slow soliton interaction with delta impurities

ABSTRACT: We study the the Gross-Pitaevskii equation with a 
          delta potential $ q \delta_0 $ where $ |q| $ is small, 
          and analyze solutions for which the initial condition is
          a soliton with initial velocity $ v_0 $. We show that
          up to time $ ( |q| + v_0^2 )^{-1/2} \log (1/|q|) $ the
          bulk of the solution is a soliton evolving to the 
          classical dynamics of a natural effective Hamiltonian,

              $ ( \xi^2 + q sech (x)^2 ) / 2 $ .

          This is joint work with Justin Holmer.




------------------------------------------------------------------
University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2006-2007 organizers:
          Pieter Blue           pblue@ math.toronto.edu
          Almut Burchard        almut@ math.toronto.edu
          Robert McCann		mccann@ math.toronto.edu
------------------------------------------------------------------