WELL-POSEDNESS AND BLOWUP FOR THE DISPERSION-MANAGED NONLINEAR SCHRÖDINGER EQUATION
Abstract
We consider the nonlinear Schrödinger equation with periodic dispersion management. We first establish global-in-time Strichartz estimates for the underlying linear equation with suitable dispersion maps. As an application, we establish a small-data scattering result for the 3d cubic equation. Finally, we use a virial argument to demonstrate the existence of blowup solutions for the 3d cubic equation with piecewise constant dispersion map.
Recommended Citation
J. Murphy and T. V. Hoose, "WELL-POSEDNESS AND BLOWUP FOR THE DISPERSION-MANAGED NONLINEAR SCHRÖDINGER EQUATION," Proceedings of the American Mathematical Society, vol. 151, no. 6, pp. 2489 - 2502, American Mathematical Society, Jun 2023.
The definitive version is available at https://doi.org/10.1090/proc/16243
Department(s)
Mathematics and Statistics
International Standard Serial Number (ISSN)
1088-6826; 0002-9939
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 American Mathematical Society, All rights reserved.
Publication Date
01 Jun 2023
