Well-posedness of dispersion managed nonlinear Schrodinger equations

초록

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.

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