University of Toronto
               PDE/Applied Math/Analysis Seminar
                 Monday November 7, 3:10-4pm
                       1230 Bahen Center      




SPEAKER:  Vitali Vougalter

TITLE:    Eigenvalues of zero energy in the linearized NLS problem  
          

ABSTRACT: 

We study a pair of neutrally stable eigenvalues of zero energy in 
the linearized NLS equation. We prove that the pair of isolated 
eigenvalues of geometric multiplicity two and algebraic multiplicity 
2N is associated with 2P negative eigenvalues of the energy operator, 
where P=N/2 if N is even and P=(N-1)/2 or P=(N+1)/2 if N is odd. When 
the potential of the linearized NLS problem is perturbed with a 
parameter continuation, we compute the exact number of unstable 
eigenvalues that bifurcate from the neutrally stable eigenvalues of 
zero energy.