Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 82, Issue 7, Pages 1150-1171Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2010.11.019
Keywords
Nonlinear Schrodinger equation; Variational approximation; Vortices; Modulational instability; Soliton collisions
Categories
Funding
- CAREER [NSF-DMS-0349023]
- Alexander von Humboldt Foundation
- [NSF-DMS-0806762]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0806762] Funding Source: National Science Foundation
Ask authors/readers for more resources
We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic-quintic nonlinear Schrodinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial and azimuthal 1D equations. A variational approach is used to predict the radial shape of the vortex soliton, using the radial equation, yielding results very close to those obtained from numerical solutions. Previously known existence bounds for the solitary vortices are recovered by means of this approach. The 1D azimuthal equation of motion is used to analyze the modulational instability of the vortex solitons. The semi-analytical predictions - in particular, the critical intrinsic frequency of the vortex soliton at the instability border - are compared to systematic 2D simulations. We also compare our findings to those reported in earlier works, which featured some discrepancies. We then perform a detailed computational study of collisions between stable vortices with different topological charges. Borders between elastic and destructive collisions are identified. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available