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TMF, 2004, Volume 138, Number 2, Pages 193–208 (Mi tmf22)  

This article is cited in 10 scientific papers (total in 10 papers)

One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model

M. O. Katanaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider the Skyrme model using the explicit parameterization of the rotation group $\mathbb S\mathbb O(3)$ through elements of its algebra. Topologically nontrivial solutions already arise in the one-dimensional case because the fundamental group of $\mathbb S\mathbb O(3)$ is $\mathbb Z_2$. We explicitly find and analyze one-dimensional static solutions. Among them, there are topologically nontrivial solutions with finite energy. We propose a new class of projective models whose target spaces are arbitrary real projective spaces $\mathbb R\mathbb P^d$.

Keywords: topological solitons, Skyrme model

DOI: https://doi.org/10.4213/tmf22

Full text: PDF file (253 kB)
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English version:
Theoretical and Mathematical Physics, 2004, 138:2, 163–176

Bibliographic databases:

Document Type: Article
Received: 17.12.2002
Revised: 14.04.2003

Citation: M. O. Katanaev, “One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model”, TMF, 138:2 (2004), 193–208; Theoret. and Math. Phys., 138:2 (2004), 163–176

Citation in format AMSBIB
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\pages 163--176
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. O. Katanaev, “Geometric theory of defects”, Phys. Usp., 48:7 (2005), 675–701  mathnet  crossref  crossref  adsnasa  isi
    2. de Berredo-Peixoto, G, “Inside the BTZ black hole”, Physical Review D, 75:2 (2007), 024004  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    3. de Berredo-Peixoto, G, “Tube dislocations in gravity”, Journal of Mathematical Physics, 50:4 (2009), 042501  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. de Berredo-Peixoto G., Katanaev M.O., Konstantinova E., Shapiro I.L., “Schrodinger equation in the space with cylindrical geometric defect and possible application to multi-wall nanotubes”, Nuovo Cimento Della Societa Italiana Di Fisica B-Basic Topics in Physics, 125:8 (2010), 915–931  zmath  isi
    5. Katanaev M.O. Mannanov I.G., “Wedge Dislocations, Three-Dimensional Gravity, and the Riemann–Hilbert Problem”, Phys. Part. Nuclei, 43:5 (2012), 639–643  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    6. Katanaev M.O., “Rotational Elastic Waves in Double Wall Tube”, Phys. Lett. A, 379:24-25 (2015), 1544–1548  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    7. Katanaev M.O., “Rotational Elastic Waves in a Cylindrical Waveguide With Wedge Dislocation”, J. Phys. A-Math. Theor., 49:8 (2016), 085202  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Katanaev M.O., “Chern–Simons Term in the Geometric Theory of Defects”, Phys. Rev. D, 96:8 (2017), 084054  crossref  isi  scopus  scopus
    9. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
    10. Mukherjee A., Kundu A., “Novel Nonlinear Wave Equation: Regulated Rogue Waves and Accelerated Soliton Solutions”, Phys. Lett. A, 383:10 (2019), 985–990  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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