Dichotomy Results for the Electromagnetic Schr\"odinger Equation
Magdalena Czubak, Ian Miller, Svetlana Roudenko
TL;DR
This paper investigates the conditions under which solutions to the electromagnetic nonlinear Schrödinger equation either exist globally or blow up in finite time in three or more dimensions.
Contribution
It provides new dichotomy results for the electromagnetic NLS, clarifying the boundary between global existence and blow-up regimes.
Findings
Established criteria for global existence of solutions.
Identified conditions leading to finite-time blow-up.
Extended previous results to higher dimensions.
Abstract
The electromagnetic nonlinear Schr\"odinger (emNLS) equation is a variant of the well-studied nonlinear Schr\"odinger equation. In this article, we consider questions of global existence or blow-up for emNLS in dimensions 3 and higher.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSpectral Theory in Mathematical Physics · Electromagnetic Simulation and Numerical Methods · Quantum Mechanics and Non-Hermitian Physics