Well–posedness of dispersion managed nonlinear Schrödinger equations

Abstract

We prove local and global well–posedness results for the Gabitov–Turitsyn or dispersion managed nonlinear Schrödinger equation with a large class of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non–zero average dispersions, respectively. Moreover, when the average dispersion is non–negative, we show that the set of ground states is orbitally stable. This covers the case of non–saturated and saturated nonlinear polarizations and yields, for saturated nonlinearities, the first proof of orbital stability.