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Conformal symmetry and the nonlinear Schrodinger equation

Pijush K. Ghosh
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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.

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Pijush K. Ghosh. 2001-10-09. Conformal symmetry and the nonlinear Schrodinger equation. https://doi.org/10.1103/physreva.65.012103

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