Transient behavior of collapsing ring solutions in the critical nonlinear Schrödinger equation

Jordan Allen-Flowers, Karl B. Glasner

Research output: Contribution to journalArticle

Abstract

The critical nonlinear Schrödinger equation (NLS) possesses nearly self-similar ring profile solutions. We address the question of whether this profile is maintained all the way until the point of singularity. A perturbative analysis of the rescaled PDE and the resulting self-similar profile uncover slow dynamics that eventually drive the ring structure to the classical peak-shaped collapse instead. A numerical scheme capable of resolving self-similar behavior to high resolutions confirms our analysis. We also consider ring-type blowup arising either from azimuthally polarized solutions of a coupled NLS system or as vortex solutions of the usual NLS. In this case, the ring profile is maintained up to the time of singularity.

Original languageEnglish (US)
Pages (from-to)53-61
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume284
DOIs
StatePublished - Sep 15 2014

Keywords

  • Blowup
  • Nonlinear Schrödinger equation
  • Self-similarity

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Transient behavior of collapsing ring solutions in the critical nonlinear Schrödinger equation'. Together they form a unique fingerprint.

  • Cite this