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On the asymptotic stability in the energy space for multi-solitons of the Landau-Lifshitz equation


Author: Yakine Bahri
Journal: Trans. Amer. Math. Soc. 370 (2018), 4683-4707
MSC (2010): Primary 35B35, 35B40, 35Q51, 35C08, 35Q56; Secondary 35C07
DOI: https://doi.org/10.1090/tran/7108
Published electronically: December 27, 2017
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Abstract: We establish the asymptotic stability of multi-solitons for the one-dimensional Landau-Lifshitz equation with an easy-plane anisotropy. The solitons have non-zero speed, are ordered according to their speeds and have sufficiently separated initial positions. We provide the asymptotic stability around solitons and between solitons. More precisely, we show that for an initial datum close to a sum of $ N$ dark solitons, the corresponding solution converges weakly to one of the solitons in the sum, when it is translated to the center of this soliton, and converges weakly to zero when it is translated between solitons.


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Additional Information

Yakine Bahri
Affiliation: Centre de Mathématiques Laurent Schwartz, École polytechnique, 91128 Palaiseau Cedex, France
Address at time of publication: Department of Mathematics and Statistics, University of Victoria, 3800 Finnerty Road, Victoria, British Columbia V8P 5C2, Canada
Email: ybahri@uvic.ca

DOI: https://doi.org/10.1090/tran/7108
Received by editor(s): April 25, 2016
Received by editor(s) in revised form: September 21, 2016
Published electronically: December 27, 2017
Additional Notes: This work was supported by a Ph.D. grant from “Région Ile-de-France”
Article copyright: © Copyright 2017 American Mathematical Society

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