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Landau-Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions

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Abstract

Using the inverse scattering method, we study the XXZ Landau-Lifshitz equation well-known in the theory of ferromagnetism. We construct all elementary soliton-type excitations and study their interaction. We also obtain finite-gap solutions (in terms of theta functions) and select the real solutions among them.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Institute of Mathematics, St. Petersburg, Russia

    R. F. Bikbaev

  2. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    A. I. Bobenko

  3. Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana, USA

    A. R. Its

Authors
  1. R. F. Bikbaev
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  2. A. I. Bobenko
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  3. A. R. Its
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Additional information

This paper is a revision at the request of the Editorial Board of Preprint No. DonFTI-84-6(81) with the same name, Donetsk Physico-Technical Institute, Academy of Sciences of the Ukrainian SSR, Donetsk, 1984.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 178, No. 2, pp. 163–219, February, 2014.

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Bikbaev, R.F., Bobenko, A.I. & Its, A.R. Landau-Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions. Theor Math Phys 178, 143–193 (2014). https://doi.org/10.1007/s11232-014-0135-4

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