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Transactions of the American Mathematical Society

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Traveling vortex helices for Schrödinger map equations


Authors: Juncheng Wei and Jun Yang
Journal: Trans. Amer. Math. Soc. 368 (2016), 2589-2622
MSC (2010): Primary 35B06, 35B40, 35J25, 35J20
DOI: https://doi.org/10.1090/tran/6379
Published electronically: July 14, 2015
MathSciNet review: 3449250
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct traveling wave solutions with vortex helix structures for the Schrödinger map equation

$\displaystyle \frac {\partial m}{\partial t}= m \times (\Delta m - m_3 \vec {e}_3)$$\displaystyle \quad \mbox {on} \ {\mathbb{R}}^3 \times {\mathbb{R}} $

of the form $ m(s_1,s_2, s_3 -\delta \vert\log \epsilon \vert\epsilon t)$ with traveling velocity $ \delta \vert\log \epsilon \vert\epsilon $ along the direction of the $ s_3$ axis. We use a perturbation approach which gives a complete characterization of the asymptotic behavior of the solutions.

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Additional Information

Juncheng Wei
Affiliation: Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2 Canada – and – Department of Mathematics, Chinese University of Hong Kong, Shatin, NT, Hong Kong
Email: wei@math.cuhk.edu.hk

Jun Yang
Affiliation: School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, People’s Republic of China – and – College of Mathematics and Computational Sciences, Shenzhen University, Nanhai Avenue 3688, Shenzhen 518060, People’s Republic of China
Email: jyang@szu.edu.cn

DOI: https://doi.org/10.1090/tran/6379
Received by editor(s): September 14, 2012
Received by editor(s) in revised form: April 18, 2013, and January 23, 2014
Published electronically: July 14, 2015
Additional Notes: The second author is the corresponding author
Article copyright: © Copyright 2015 American Mathematical Society

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