Modified Scattering for a Dispersion-Managed Nonlinear Schrödinger Equation
We prove sharp L∞ decay and modified scattering for a one-dimensional dispersion-managed cubic nonlinear Schrödinger equation with small initial data chosen from a weighted Sobolev space. Specifically, we work with an averaged version of the dispersion-managed NLS in the strong dispersion management regime. The proof adapts techniques from Hayashi and Naumkin (Am. J. Math. 120(2):369-389, 1998) and Kato and Pusateri (Differ Integral Equ 24(9-10):923-940, 2011), which established small-data modified scattering for the standard 1d cubic NLS.
J. Murphy and T. Van Hoose, "Modified Scattering for a Dispersion-Managed Nonlinear Schrödinger Equation," Nonlinear Differential Equations and Applications, vol. 29, no. 1, article no. 1, Springer, Jan 2022.
The definitive version is available at https://doi.org/10.1007/s00030-021-00731-6
Mathematics and Statistics
Keywords and Phrases
Dispersion-Managed NLS; Modified Scattering
International Standard Serial Number (ISSN)
Article - Journal
© 2021 The Author(s), under exclusive licence to Springer Nature Switzerland, All rights reserved.
01 Jan 2022