DE Seminar: On ill-posedness for the dispersion-managed nonlinear Schrödinger equation

The dispersion-managed nonlinear Schrödinger equation models the propagation of pulses through long-haul optical fibers, where the dispersion profile—and hence the focusing or defocusing nature—varies periodically. When the dispersion oscillates rapidly, this leads to the Gabitov–Turitsyn equation, a nonlocal nonlinear Schrödinger equation obtained by evolving the nonlinearity under the linear flow and averaging in time.

Despite substantial attention in physics and numerics, rigorous results for this model are rare and the sharp well-posedness theory has remained largely unclear. In this talk, we present recent results that identify a threshold for well-posedness, below which contraction mapping arguments fail, and a second, distinct threshold below which norm inflation can be shown under suitable restrictions.