Sonin's argument, the shape of solitons, and the most stably singular matrix

zbMATH Open1437.35144arXiv1811.01836MaRDI QIDQ5213213

Monica Visan, Rowan Killip

Publication date: 31 January 2020

Abstract: We present two adaptations of an argument of Sonin, which is known to be a powerful tool for obtaining both qualitative and quantitative information about special functions. Our particular applications are as follows: (i) We give a rigorous formulation and proof of the following assertion about focusing NLS in any dimension: The spatial envelope of a spherically symmetric soliton in a repulsive potential is a non-increasing function of the radius. (ii) Driven by the question of determining the most stably singular matrix, we determine the location of the maximal eigenvalue density of an $nimesn$ GUE matrix. Strikingly, in even dimensions, this maximum is emph{not} at zero.

Full work available at URL: https://arxiv.org/abs/1811.01836

zbMATH Keywords

focusing NLSlocation of the maximal eigenvalue densityspatial envelope of a sperically symmetric soliton

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Random matrices (algebraic aspects) (15B52) Random linear operators (47B80) Soliton solutions (35C08)

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