CRITICAL NONLINEAR SCHRÖDINGER EQUATIONS WITH AND WITHOUT HARMONIC POTENTIAL

Rémi Carles

Type: Article

Publication Date: 2002-10-01

Citations: 75

DOI: https://doi.org/10.1142/s0218202502002215

Abstract

We use a change of variables that turns the critical nonlinear Schrödinger equation into the critical nonlinear Schrödinger equation with isotropic harmonic potential, in any space dimension. This change of variables is isometric on L 2 , and bijective on some time intervals. Using the known results for the critical nonlinear Schrödinger equation, this provides information for the properties of Bose–Einstein condensate in space dimension one and two. We discuss in particular the wave collapse phenomenon.

Locations

Mathematical Models and Methods in Applied Sciences - View
arXiv (Cornell University) - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View

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+	The maximal kinematical invariance group of the harmonic oscillator	1973	U. Niederer
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