Mathematical challenges from non-linear fiber optics

In optical fiber communications the technique of 'dispersion management' was invented in the 90's to create stable pulses in glass fiber cables by periodically varying the dispersion along the cable. This idea turned out to be enormously fruitful in allowing for ultra high-speed data transfer through optical fibers over intercontinental distances and the dispersion management technique is now widely used commercially (as a test: google `dispersion management' and you'll get an overwelming amount of hits).

The propagation of pulses through an dispersion managed glass fiber cable is described by the Gabitov-Turitsyn equation, which is a non-local version of the non-linear Schr\"odinger equation. It has been extensively studied numerically and on the level of theoretical physics, but rigorous results are rare. We describe very recent work on the decay and regularity properties of stationary solutions of the Gabitov-Turitsyn equation.

This is joint work with Young-Ran Lee.