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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 178, Number 2, Pages 163–219
DOI: https://doi.org/10.4213/tmf8532 (Mi tmf8532) 		 
This article is cited in 19 scientific papers (total in 19 papers)

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

R. F. Bikbaev, A. I. Bobenkoa, A. R. Itsb

a Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
b Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, USA
Full-text PDF (1060 kB) Citations (19)
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DOI: https://doi.org/10.4213/tmf8532
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.
Received: 07.03.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 178, Issue 2, Pages 143–193
DOI: https://doi.org/10.1007/s11232-014-0135-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. F. Bikbaev, A. I. Bobenko, A. R. Its, “Landau–Lifshitz equation, uniaxial anisotropy case: Theory of exact solutions”, TMF, 178:2 (2014), 163–219; Theoret. and Math. Phys., 178:2 (2014), 143–193
Citation in format AMSBIB
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    • This publication is cited in the following 19 articles:
    1. Harini Desiraju, Alexander Its, Andrei Prokhorov, “Nonlinear steepest descent on a torus: a case study of the Landau–Lifshitz equation”, Nonlinearity, 38:4 (2025), 045023  crossref
    2. Žiga Krajnik, Johannes Schmidt, Enej Ilievski, Tomaž Prosen, “Dynamical Criticality of Magnetization Transfer in Integrable Spin Chains”, Phys. Rev. Lett., 132:1 (2024)  crossref
    3. André de Laire, “Recent results for the Landau–Lifshitz equation”, SeMA, 79:2 (2022), 253  crossref
    4. Miao Yu., Ilievski E., Gamayun O., “Semi-Classical Quantisation of Magnetic Solitons in the Anisotropic Heisenberg Quantum Chain”, SciPost Phys., 10:4 (2021)  crossref  mathscinet  isi
    5. Habibullin I.T. Khakimova A.R., “Invariant Manifolds and Separation of the Variables For Integrable Chains”, J. Phys. A-Math. Theor., 53:38 (2020), 385202  crossref  mathscinet  isi
    6. Li R., Geng X., Xue B., “A Generalization of the Landau-Lifschitz Equation: Breathers and Rogue Waves”, J. Nonlinear Math. Phys., 27:2 (2020), 279–294  crossref  mathscinet  isi
    7. Zabolotskii A.A., “Nonlinear Electromagnetic Pulse Isolator”, Phys. Rev. A, 101:5 (2020), 053837  crossref  mathscinet  isi  scopus
    8. Kiselev V.V. Raskovalov A.A., “Solitons in the Domain Structure of a Two-Axis Ferromagnet”, Chaos Solitons Fractals, 135 (2020), UNSP 109803  crossref  mathscinet  isi
    9. Zabolotskii A.A., “Few-Cycle Solitons in a Dispersive Medium With a Permanent Dipole Moment”, Phys. Rev. E, 102:1 (2020), 012214  crossref  mathscinet  isi
    10. Kiselev V.V. Raskovalov A.A., “Soliton Dynamics in the Domain Structure of a Biaxial Ferromagnet”, Low Temp. Phys., 46:11 (2020), 1098–1107  crossref  mathscinet  isi  scopus
    11. Zabolotskii A.A., “Joint Effect of the Dipole-Dipole Interaction and Constant Dipole Moment on the Shape of the Field Pulse Without An Envelope”, J. Exp. Theor. Phys., 131:4 (2020), 520–529  crossref  isi
    12. O. Gamayun, Yu. Miao, E. Ilievski, “Domain-wall dynamics in the Landau-lifshitz magnet and the classical-quantum correspondence for spin transport”, Phys. Rev. B, 99:14 (2019), 140301  crossref  mathscinet  isi  scopus
    13. S. Komineas, Ch. Melcher, S. Venakides, “Traveling domain walls in chiral ferromagnets”, Nonlinearity, 32:7 (2019), 2392–2412  crossref  mathscinet  isi
    14. A. A. Zabolotskii, “Exciton dynamics in a helical molecular aggregate”, J. Exp. Theor. Phys., 127:3 (2018), 448–454  crossref  crossref  isi  elib  scopus
    15. F. Han, G. Yang, “Some explicit solutions of the Landau-Lifshitz equation for anisotropic ferromagnets”, Math. Meth. Appl. Sci., 41:17, SI (2018), 7839–7851  crossref  mathscinet  zmath  isi
    16. de Laire A., Gravejat Ph., “Stability in the Energy Space For Chains of Solitons of the Landau-Lifshitz Equation”, J. Differ. Equ., 258:1 (2015), 1–80  crossref  mathscinet  zmath  adsnasa  isi  scopus
    17. Zhou T., Stone M., “Solitons in a Continuous Classical Haldane-Shastry Spin Chain”, Phys. Lett. A, 379:43-44 (2015), 2817–2825  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    18. André de Laire, Philippe Gravejat, “Stabilité des solitons de l'équation de Landau-Lifshitz à anisotropie planaire”, Séminaire Laurent Schwartz — EDP et applications, 2015, 1  crossref
    19. Denisov S.I., Lyutyy T.V., Pedchenko B.O., Babych H.V., “Eddy Current Effects in the Magnetization Dynamics of Ferromagnetic Metal Nanoparticles”, J. Appl. Phys., 116:4 (2014), 043911  crossref  adsnasa  isi  scopus
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