Well-posedness of dispersion managed nonlinear Schrödinger equations

2020/03/20 by Choi, Mi-Ran, Hundertmark, Dirk, Lee, Young-Ran · 1 citation
#35A01 #35B30 #35B35 #35Q55 #35Q60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.09076

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). 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.

Cited by

• On ill-posedness for the Gabitov--Turitsyn equation

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