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A Planar Skyrme-Like Model

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The sine-Gordon Model and its Applications

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 10))

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Abstract

After an introduction of solitons with emphasis in elementary particle theory, we present a non-linear O(3) model in (2 + 1) dimensions modified by the addition of both a potential-like and a Skyrme-like term. We study some basic scattering properties of the model via numerical simulation using a general field configuration. The skyrmion-scattering is found to be quasi-elastic, the skyrmions’ energy density profiles remaining unscathed after collisions. In low-energy processes the skyrmions exhibit back-scattering, while at larger energies they scatter at right angles. These results confirm those obtained in previous investigations, in which a similar problem was studied for a different choice of the potential-like term.

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References

  1. C.N. Yang, R.L. Mills, Phys. Rev. 96, 191 (1954)

    Article  MathSciNet  ADS  Google Scholar 

  2. F. Englert, R. Brout, Phys. Rev. Lett. 13, 321 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  3. P.W. Higgs, Phys. Rev. 13, 508 (1964)

    MathSciNet  ADS  Google Scholar 

  4. G.S. Guralnik, C.R. Hagen, T.W.B. Kibble, Phys. Rev. Lett. 13, 585 (1964)

    Article  ADS  Google Scholar 

  5. J.L. Miller, Phys. Today 65(12), 9 (2012)

    Article  Google Scholar 

  6. R. Rajaraman, Solitons and Instantons (North-Holland, New York, 1987)

    MATH  Google Scholar 

  7. L.V. Yakushevich, Q. Rev. Biophys. 20, 201 (1993)

    Google Scholar 

  8. D. Iagolnitzer (ed.), Proceedings of the International Congress of Mathematical Physics, vol. 691 (International Press, Paris, 1994)

    Google Scholar 

  9. E. Desurvire, Phys. Today 41(1), 20 (1994)

    Article  Google Scholar 

  10. J.S. Russell, Report of the Fourteenth Meeting of the British Association for the Advancement of Science, York, 1844, pp. 311–390

    Google Scholar 

  11. D.J. Korteweg, G. de Vries, Philos. Mag. Ser. 5 39, 422 (1895)

    Google Scholar 

  12. N.J. Zabusky, M.D. Kruskal, Phys. Rev. Lett. 15, 240 (1965)

    Article  MATH  ADS  Google Scholar 

  13. R.M. Miura, C.S. Gardner, M.D. Kruskal, J. Math. Phys. 9, 1204 (1968)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. V.E. Zakharov, A. Shabat, Sov. Phys. JETP 34, 62 (1972)

    MathSciNet  ADS  Google Scholar 

  15. A. Barone, F. Esposito, C.J. Magee, A.C. Scott, Riv. Nuovo Cimento 1, 227 (1971)

    Article  Google Scholar 

  16. A.C. Scott, F.Y.F. Chu, D.W. MacLaughlin, Proc. IEEE 61, 1443 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  17. A.M. Grundland, A.J. Hariton, L. Šnobi, J. Phys. A: Math. Theor. 42, 335203 (2009)

    Article  Google Scholar 

  18. J. Hruby, Czech. Jour. Phys. B 32, 1100 (1982)

    Article  MathSciNet  ADS  Google Scholar 

  19. E. Witten, Phys. Rev. D 16, 2991 (1977)

    Article  ADS  Google Scholar 

  20. C.S. Gardner, J.M. Greene, M.D. Kruskal, R.M. Miura, Phys. Rev. Lett. 19, 1095 (1967)

    Article  ADS  Google Scholar 

  21. G.L. Lamb, Phys. Lett. A 25, 181 (1967)

    Article  ADS  Google Scholar 

  22. R. Hirota, Phys. Rev. Lett. 27, 1192 (1971)

    Article  MATH  ADS  Google Scholar 

  23. A. Davey, K. Stewardson, Proc. Roy. Soc. Lond. A 338, 101 (1974)

    Article  MATH  ADS  Google Scholar 

  24. S. Novikov, Theory of Solitons (Consultants Bureau, New York, 1984)

    MATH  Google Scholar 

  25. N. Manton, P. Sutcliffe, Topological Solitons (Cambridge University Press, Cambridge, 2004)

    Book  MATH  Google Scholar 

  26. G.’t-Hooft, Nucl. Phys. B 79, 276 (1974)

    Google Scholar 

  27. A.M. Polyakov, JETP Lett. 20, 194 (1974)

    ADS  Google Scholar 

  28. A.M. Polyakov, Nucl. Phys. B 120, 429 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  29. S. Coleman, in The Whys of Subnuclear Physics, ed. by A. Zichichi (Plenum Press, New York, 1979)

    Google Scholar 

  30. T.H.R. Skyrme, Nucl. Phys. 31, 556 (1962)

    Article  MathSciNet  Google Scholar 

  31. G. Holzwarth, B. Schwesinger, Rep. Prog. Phys. 49, 825 (1986)

    Article  ADS  Google Scholar 

  32. E. Witten, Nucl. Phys. B 160, 57 (1979)

    Article  MathSciNet  ADS  Google Scholar 

  33. A. Chodos, C.B. Thor, Phys. Rev. D 12, 2733 (1975)

    Article  ADS  Google Scholar 

  34. M. Gell-Mann, M. Levy, Nuovo Cimento 16, 705 (1960)

    Article  MATH  MathSciNet  Google Scholar 

  35. E. Brown Gerald (ed.), Selected Papers, with Commentary, of Tony Hilton Royle Skyrme (World Scientific, River Edge, 1994)

    Google Scholar 

  36. V.G. Makhankov, The Skyrme Model (Springer, New York, 1993)

    Book  Google Scholar 

  37. J. Eells, J.C. Wood, Topology 15, 263 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  38. I. Dzyaloshinskii, A. Polyakov, P. Wiegmann, Phys. Lett. A 127, 112 (1988)

    Article  ADS  Google Scholar 

  39. A.G. Green, I.I. Kogan, A.M. Tsvelik, Phys. Rev. B 53, 6981 (1996)

    Article  ADS  Google Scholar 

  40. N. Steenrod, The Topology of Fiber Bundles (Princeton University Press, Princeton, 1951)

    Google Scholar 

  41. M. Nakahara, Geometry, Topology and Physics (IOP publishing, Bristol/Philadelphia, 1990)

    Book  MATH  Google Scholar 

  42. L.V. Ahlfors, Complex Analysis (McGraw Hill, New York, 1953)

    MATH  Google Scholar 

  43. A.A. Belavin, A.M. Poliakov, JETP Lett. 22, 245 (1975)

    ADS  Google Scholar 

  44. G. Woo, J. Math. Phys. 18, 1264 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  45. A.M. Din, W.J. Zakrzewski, Nucl. Phys. B 174, 397 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  46. R.J. Cova, W.J. Zakrzewski, Nonlineartity 10, 1305 (1997)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  47. R.A. Leese, M. Peyrard, W.J. Zakrzewski, Nonlinearity 3, 387 (1990)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  48. R.A. Leese, M. Peyrard, W.J. Zakrzewski, Nucl. Phys. B 344, 33 (1990)

    Article  ADS  Google Scholar 

  49. W.J. Zakrzewski, Nonlinearity 4, 429 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  50. R.A. Leese, M. Peyrard, W.J. Zakrzewski, Nonlinearity 3, 773 (1990)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  51. J.A. Azcárraga, M.S. Rashid, W.J. Zakrzewski, J. Math. Phys. 32, 1921 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  52. B. Piette, W.J. Zakrzewski, Nucl. Phys. B 393, 65 (1993)

    Article  ADS  Google Scholar 

  53. P.M. Sutcliffe, Nonlinearity 4, 1109 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  54. D.K. Campbell, M. Peyrard, Physica D 18, 47 (1986)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  55. E.P.S. Shellar, P.J. Ruback, Phys. Lett. B 209, 262 (1988)

    Article  ADS  Google Scholar 

  56. M.F. Atiyah, N.J. Hitchin, The Geometry and Dynamics of Magnetic Monopoles (Princenton University Press, Princenton, 1988)

    MATH  Google Scholar 

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Acknowledgements

The author is greatly indebted to Dr. David Amundsen and Dr. Patrick Farrell for their hospitality at the School of Mathematics and Statistics, Carleton University. He is also very grateful to Dr. Amundsen for helpful research discussions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K2E 7E8

    Ramón J. Cova

  2. Department of Physics, The University of Zulia, Maracaibo, Venezuela

    Ramón J. Cova

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  1. Ramón J. Cova
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Correspondence to Ramón J. Cova .

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Editors and Affiliations

  1. Departamento de Físíca Aplicada I, University of Sevilla, Sevilla, Spain

    Jesús Cuevas-Maraver

  2. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Panayotis G. Kevrekidis

  3. Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, USA

    Floyd Williams

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Cova, R.J. (2014). A Planar Skyrme-Like Model. In: Cuevas-Maraver, J., Kevrekidis, P., Williams, F. (eds) The sine-Gordon Model and its Applications. Nonlinear Systems and Complexity, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-319-06722-3_10

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  • DOI: https://doi.org/10.1007/978-3-319-06722-3_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06721-6

  • Online ISBN: 978-3-319-06722-3

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