Well–posedness of dispersion managed nonlinear Schrödinger equations

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