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arXiv.org e-Print Archive
Preprint . 2008
Data sources: arXiv.org e-Print Archive
SIAM Journal on Applied Mathematics
Article . 2009 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2008
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SIAM Journal on Applied Mathematics
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A Numerical Study of the Self-Similar Solutions of the Schrödinger Map

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2009Embargo end date: 01 Jan 2008Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Applied Mathematics, volume 70, pages 1,047-1,077 (issn: 0036-1399, eissn: 1095-712X, Copyright policy )
Authors: Luis Vega; Carlos J. García-Cervera; F. de la Hoz;

doi: 10.1137/080741720 , 10.48550/arxiv.0812.1011

arXiv: http://arxiv.org/abs/0812.1011

A Numerical Study of the Self-Similar Solutions of the Schrödinger Map

Abstract

We present a numerical study of the self-similar solutions of the Localized Induction Approximation of a vortex filament. These self-similar solutions, which constitute a one-parameter family, develop a singularity at finite time. We study a number of boundary conditions that allow us reproduce the mechanism of singularity formation. Some related questions are also considered.

Related Organizations
Keywords

35Q55, 65D10, 65N35, 65T50, 76B47, Mathematics - Analysis of PDEs, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Analysis of PDEs (math.AP)

  • BIP!
    Impact byBIP!
    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 18
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
18
Top 10%
Top 10%
Average
Green