Well-posedness of dispersion managed nonlinear Schrodinger equations

We prove local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schrodinger 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. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

We establish local and global well-posedness results for the Gabitov-Turitsyn or dispersion managed nonlinear Schrodinger equation with a wide range of nonlinearities and arbitrary average dispersion on L2(R) and H1(R) for zero and non-zero average dispersions, respectively. Additionally, we demonstrate the orbital stability of the set of ground states when the average dispersion is non-negative. This result covers both non-saturated and saturated nonlinear polarizations, and provides the first proof of orbital stability for saturated nonlinearities.