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Theoretical and Mathematical Physics

, Volume 178, Issue 2, pp 143–193 | Cite as

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

  • R. F. Bikbaev
  • A. I. Bobenko
  • A. R. Its
Article

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.

Keywords

multisoliton solution ferromagnetism finite-gap integration theta function 

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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  • R. F. Bikbaev
    • 1
  • A. I. Bobenko
    • 2
  • A. R. Its
    • 3
  1. 1.St. Petersburg Department of the Steklov Institute of MathematicsSt. PetersburgRussia
  2. 2.Institut für MathematikTechnische Universität BerlinBerlinGermany
  3. 3.Department of Mathematical SciencesIndiana University-Purdue University IndianapolisIndianapolisUSA

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