Well-posedness and blowup for the dispersion-managed nonlinear Schr\"odinger equation
Analysis of PDEs
2023-05-11 v1
Abstract
We consider the nonlinear Schr\"odinger 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 cubic equation. Finally, we use a virial argument to demonstrate the existence of blowup solutions for the cubic equation with piecewise constant dispersion map.
Keywords
Cite
@article{arxiv.2110.08372,
title = {Well-posedness and blowup for the dispersion-managed nonlinear Schr\"odinger equation},
author = {Jason Murphy and Tim Van Hoose},
journal= {arXiv preprint arXiv:2110.08372},
year = {2023}
}
Comments
13 pages, 1 figure