Skip to main content

On Some Solutions of Certain Versions of “Sigma” Model and Some Skyrme-Like Models

  • Conference paper
Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

  • 1179 Accesses

Abstract

Some results concerning certain versions of “sigma” model and some Skyrme-like models, are presented.

This paper is based on a talk, delivered by the Author at ISAAC 2013 Congress in Kraków, Poland.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. C. Adam, P. Klimas, J. Sanchez-Guillen, A. Wereszczyński, Phys. Rev. D 80, 105013 (2009)

    Article  Google Scholar 

  2. C. Adam, T. Romańczukiewicz, J. Sanchez-Guillen, A. Wereszczyński, Phys. Rev. D 81, 085007 (2010)

    Article  Google Scholar 

  3. A.A. Belavin, A.M. Polyakov, JETP Lett. 22, 245 (1975)

    Google Scholar 

  4. A.A. Belavin, A.M. Polyakov, A.S. Schwartz, Yu.S. Tyupkin, Phys. Lett. B 59, 85 (1975)

    Article  MathSciNet  Google Scholar 

  5. I. Białynicki-Birula, On the stability of solitons, in Nonlinear Problems of Theoretical Physics (Springer, Berlin, 1979), p. 15

    Chapter  Google Scholar 

  6. Yu.A. Bobkov, Differ. Uravn. 45(6), 888 (2009)

    MathSciNet  Google Scholar 

  7. Yu.A. Bobkov, Differ. Equ. 45(6), 907 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. E.B. Bogomolny, Sov. J. Nucl. Phys. 24, 861 (1976)

    Google Scholar 

  9. M.M. Enikova, V.I. Karloukovski, C.I. Velchev, Nucl. Phys. B 151, 172 (1979)

    Article  MathSciNet  Google Scholar 

  10. N. Erouguine, C.R. Doklady, Acad. Sci. URSS (N. S.) 42, 371 (1944) (in French)

    Google Scholar 

  11. N.P. Erugin, Dokl. Akad. Nauk USSR 42, 371 (1944)

    Google Scholar 

  12. N.P. Erugin, M.M. Smirnov, Differ. Uravn. 17(5), 853 (1981)

    MATH  MathSciNet  Google Scholar 

  13. P. Eslami, M. Sarbishaei, W.J. Zakrzewski, Nonlinearity 13, 1867 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. L.D. Faddeev, A.J. Niemi, Nature 387, 58 (1997)

    Article  Google Scholar 

  15. L.A. Ferreira, P. Klimas, J. High Energy Phys. 10, 008 (2010)

    Article  MathSciNet  Google Scholar 

  16. L.A. Ferreira, P. Klimas, W.J. Zakrzewski, J. High Energy Phys. 12, 098 (2011). arXiv:1111.2338 [hep-th]

    Article  Google Scholar 

  17. L.M. Galonen, Izv. Akad. Nauk SSSR 21, 53 (1957)

    MATH  MathSciNet  Google Scholar 

  18. T. Gisiger, M.B. Paranjape, Phys. Rev. D 55, 7731 (1997)

    Article  Google Scholar 

  19. T. Gisiger, M.B. Paranjape, in Solitons: Properties, Dynamics, Interactions, Applications, vol. 183, ed. by R. MacKenzie, M.B. Paranjape, W.J. Zakrzewski (Springer, Berlin, 2000)

    Google Scholar 

  20. J. Hietarinta, P. Salo, Phys. Rev. D 62, 081701 (2000)

    Article  Google Scholar 

  21. A. Hosoya, Prog. Theor. Phys. 59, 1781 (1978)

    Article  Google Scholar 

  22. J. Jäykkä, M. Speight, P. Sutcliffe, Proc. R. Soc. A 468, 1085 (2012)

    Article  Google Scholar 

  23. P.T. Jochym, K. Sokalski, J. Phys. A 26, 3837 (1993)

    Article  MathSciNet  Google Scholar 

  24. M. Karliner, I. Hen, Nonlinearity 21, 399 (2008)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  26. W.G. Makhankov, Yu.P. Rybakov, W.I. Sanyuk, Skyrme Models and Solitons in Physics of Hadrons (1989) (in Russian)

    Google Scholar 

  27. S.V. Meleshko, Methods for Constructing Exact Solutions of Partial Differential Equations: Mathematical and Analytical Techniques with Applications to Engineering (Springer, Berlin, 2005)

    Google Scholar 

  28. O.F. Menshikh, M.I. Timoshin, The International Conference MOGRANE 2000. http://www.bth.se/ihn/alga.nsf/attachments/d92MT.pdf/tile/d92MT.pdf

  29. B.M.A.G. Piette, B.J. Schroers, W.J. Zakrzewski, Chaos Solitons Fractals 5, 2495 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  30. T.H.R. Skyrme, Proc. R. Soc. A 260, 127 (1961)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  32. T.H.R. Skyrme, J. Math. Phys. 12, 1735 (1971)

    Article  MathSciNet  Google Scholar 

  33. S. Sobolev, Travaux Inst. Fiz. Mat. Stekloff, Acad. Sci. USSR, 259 (1934)

    Google Scholar 

  34. S. Sobolev, Tr. Fiz.-Mat. Inst. Steklova 5, 259 (1934)

    Google Scholar 

  35. K. Sokalski, Acta Phys. Pol. A 56, 571 (1979)

    MathSciNet  Google Scholar 

  36. K. Sokalski, T. Wietecha, Z. Lisowski, Acta Phys. Pol. B 32, 17 (2001)

    MATH  MathSciNet  Google Scholar 

  37. K. Sokalski, T. Wietecha, Z. Lisowski, Acta Phys. Pol. B 32, 2771 (2001)

    MathSciNet  Google Scholar 

  38. K. Sokalski, Ł. Stȩpień, D. Sokalska, J. Phys. A 35, 6157 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  39. S.L. Sondhi, A. Karlhede, S.A. Kivelson, E.H. Rezayi, Phys. Rev. B 47, 16419 (1993)

    Article  Google Scholar 

  40. J.M. Speight, J. Phys. A 43, 405201 (2010)

    Article  MathSciNet  Google Scholar 

  41. N.T. Stel’mashuk, Ukr. Mat. Zh. 24(1), 115 (1971)

    Google Scholar 

  42. Ł. Stȩpień, Bogomolny decomposition in the context of the concept of strong necessary conditions. Ph.D. thesis, Jagiellonian University, Kraków, Poland (2003) (in Polish)

    Google Scholar 

  43. Ł.T. Stȩpień, J. Comput. Appl. Math. 233, 1607 (2010)

    Article  MathSciNet  Google Scholar 

  44. Ł.T. Stȩpień (2012). arXiv:1208.2905

  45. Ł.T. Stȩpień, On bogomolny decompositions for the baby skyrme models, in Geometric Methods in Physics, XXXI Workshop 2012, Trends in Matematics, 229–237, 27 April 2012 (Birkhäuser, Basel, 2013). arXiv:1204.6194v1

    Google Scholar 

  46. Ł. Stȩpień, D. Sokalska, K. Sokalski, J. Nonlinear Math. Phys. 16, 25 (2009)

    Article  MathSciNet  Google Scholar 

  47. P. Voruganti, Phys. Lett. B 223, 181 (1989)

    Article  MathSciNet  Google Scholar 

  48. N.R. Walet, T. Weidig, Europhys. Lett. 55, 633 (2001)

    Article  Google Scholar 

  49. A. Wereszczyński, Phys. Lett. B 621, 201 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  50. Y. Yang, Solitons in Field Theory and Nonlinear Analysis (Springer, Berlin, 2001)

    Book  MATH  Google Scholar 

Download references

Acknowledgement

The author thanks Dr. hab. A. Wereszczyński for interesting discussions about the restricted baby Skyrme models, carried out in 2010. The author also thanks Dr. Z. Lisowski for some interesting remarks.

The participation of the author, in “ISAAC 2013 Congress”, was possible owing to the financial support, provided by The Pedagogical University of Cracow.

The computations were carried out by using Waterloo MAPLE 17 Software on the computer mars (No. of grant: MNiI/IBM BC HS21/AP/057/2008), in ACK CYFRONET-AGH in Kraków. This research was supported also by PL-Grid Infrastructure.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Łukasz T. Stȩpień .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Stȩpień, Ł.T. (2015). On Some Solutions of Certain Versions of “Sigma” Model and Some Skyrme-Like Models. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_32

Download citation

Publish with us

Policies and ethics