Gino Biondini
University at Buffalo, State University of New York
Title
Spectral theory for Dirac operators with periodic coefficients: Some recent results and applications to the focusing nonlinear Schrodinger equation
Abstract
The behavior of solutions of integrable nonlinear PDEs with periodic boundary conditions is receiving renewed interest in recent years, due in part to the connection with the emerging subject of soliton and breather gases. In this talk I will review some recent results concerning a one-dimensional periodic Dirac operator, which is asssociated to the spectral problem for the focusing nonlinear Schrodinger equation. These include: (i) An asymptotic characterization of the spectrum in the semiclassical limit; (ii) The characterization of a two-parameter class of exactly solvable elliptic potentials, (iii) The development of the inverse spectral problem via a Riemann-Hilbert problem approach, and (iv) The characterization of behavior of solutions in the semiclassical limit.
