Conformal symmetry and the nonlinear Schrodinger equation
Condensed Matter
2009-11-07 v3 High Energy Physics - Theory
Pattern Formation and Solitons
Abstract
We show that the width of the wave-packet of a class of generalized nonlinear Schrodinger equations (NLSE) trapped in an arbitrary time-dependent harmonic well in any dimensions is universally determined by the same Hill's equation. This class of generalized NLSE is characterized by a dynamical O(2,1) symmetry in absence of the trap. As an application, we study the dynamical instabilities of the rotating as well as non-rotating Bose-Einstein condensates in one and two dimensions. We also show exact extended parametric resonance in a non-relativistic Chern-Simons theory producing a gauged NLSE.
Keywords
Cite
@article{arxiv.cond-mat/0102488,
title = {Conformal symmetry and the nonlinear Schrodinger equation},
author = {Pijush K. Ghosh},
journal= {arXiv preprint arXiv:cond-mat/0102488},
year = {2009}
}
Comments
RevTeX, 5 pages (v1); Added a footnote and an example (v2); Updated references, to appear in Physical Review A (v3)