We consider the Cauchy problem for dispersion-managed nonlinear Schrödinger equations, where the dispersion map is assumed to be periodic and piecewise constant in time. We establish local and global well-posedness results and the possibility of finite time blow-up. In addition, we shall study the scaling limit of fast dispersion management and establish convergence to an effective model with averaged dispersion.
Paolor Antonelli. ean-Claude Saut. Christof Sparber. "Well-Posedness and averaging of NLS with time-periodic dispersion management." Adv. Differential Equations 18 (1/2) 49 - 68, January/February 2013. https://doi.org/10.57262/ade/1355867481