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29 March 2024
 
  » arxiv » cond-mat/9809203

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Stationary states of the Gross-Pitaevskii equation with linear counterpart
Roberto D’Agosta ; Boris A. Malomed ; Carlo Presilla ;
Date 14 Sep 1998
Journal Phys. Lett. A 275, 424-434 (2000)
Subject Condensed Matter; Mathematical Physics; Pattern Formation and Solitons | cond-mat math-ph math.MP nlin.PS patt-sol quant-ph
AbstractWe study the stationary solutions of the Gross-Pitaevskii equation that reduce, in the limit of vanishing non-linearity, to the eigenfunctions of the associated Schrödinger equation. By providing analytical and numerical support, we conjecture an existence condition for these solutions in terms of the ratio between their proper frequency (chemical potential) and the corresponding linear eigenvalue. We also give approximate expressions for the stationary solutions which become exact in the opposite limit of strong non-linearity. For one-dimensional systems these solutions have the form of a chain of dark or bright solitons depending on the sign of the non-linearity. We demonstrate that in the case of negative non-linearity (attractive interaction) the norm of the solutions is always bounded for dimensions greater than one.
Source arXiv, cond-mat/9809203
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