EVENT DETAILS AND ABSTRACT

Title: Linear instability of solitary waves in nonlinear Dirac equation
Speaker: Andrew Comech
Speaker Info: Texas A&M
Brief Description:
Special Note:
Abstract:

We study the linear instability of solitary wave solutions to the nonlinear Dirac equation (known to physicists as the Soler model). That is, we linearize the equation at a solitary wave and examine the presence of eigenvalues with positive real part.

We show that the linear instability of the small amplitude solitary waves is described by the Vakhitov-Kolokolov stability criterion which was obtained in the context of the nonlinear Schroedinger equation: small solitary waves are linearly unstable in dimensions 3, and generically linearly stable in 1D.

A particular question is on the possibility of bifurcations of eigenvalues from the continuous spectrum; we address it using the limiting absorption principle and the Carleman inequality.

The method is applicable to other systems, such as the Dirac-Maxwell system.

Some of the results are obtained in collaboration with Nabile Boussaid, Université de Franche-Comté, and Stephen Gustafson, University of British Columbia.