WELL-POSEDNESS AND BLOWUP FOR THE DISPERSION-MANAGED NONLINEAR SCHRÖDINGER EQUATION

Author

Jason Murphy, Missouri University of Science and TechnologyFollow
Tim Van Hoose

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