Skip to main content
SpringerLink
Log in

The Collision of Two-Kinks Revisited: the Creation of Kinks and Lump-Like Defects as Metastable States

  • Particles and Fields
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We present a more detailed numerical investigation of the head-on collision of a two-kink/two-antikink system. We identified the escape of oscillon-like configurations as a pair of kinks of the standard ϕ4 model moving apart from each other. New pieces of evidence support that the lump-like defects can emerge from the two-kink interaction to form metastable configurations. Moreover, these configurations signalize the windows of escape that have a fractal structure similar to the n-bounce sequence when the kinks of ϕ4 interact. As the last piece of the numerical experiment, we show that by perturbing conveniently a lump-like defect, it is possible to recover another lump-like configuration as a metastable configuration.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. In the collision of kinks, this velocity is called the critical velocity.

References

  1. F. Abdullaevv, Phys. Rep. 179, 1 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  2. Y. Kivshar, B. Malomed, Rev. Mod. Phys. 61, 763 (1989)

    Article  ADS  Google Scholar 

  3. R. Rajaram. Solitons and instantons (World Scientific, Singapore, 1989)

    Google Scholar 

  4. A. Vilenkin, E. P. Shellard. Cosmic strings and other topological defects (Cambridge University Press, Cambridge, 1994)

    MATH  Google Scholar 

  5. A. Avelar, D. Bazeia, L. Losano, Eur. Phys. J. C. 55, 133 (2008)

    Article  ADS  Google Scholar 

  6. Y. Brihaye, A. Cisterna, B. Hartmann, G. Luchini, Phys. Rev. D. 92, 124061 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  7. D. Walgraef. Spatio-temporal pattern formation (Springer-Verlag, New York, 1997)

    Book  Google Scholar 

  8. G. Rosen, J. Math. Phys. 9, 996 (1968)

    Article  ADS  Google Scholar 

  9. T.D. Lee, Particle physics and introduction to field theory (Harwood Academic Publishers) (1982)

  10. S. Coleman, Nucl. Phys. B. 262, 263 (1985)

    Article  ADS  Google Scholar 

  11. B. Fuchs, E. W. Mielke, MNRAS. 350, 707 (2004)

    Article  ADS  Google Scholar 

  12. T. S. Mendonça, H. P. de Oliveira, J. High Energ. Phys. 9, 2015. arXiv:1502.03870(2015)

  13. D. Bazeia, J. Menezes, R. Menezes, Phys. Rev. Lett. 24, 241601 (2003)

    Article  ADS  Google Scholar 

  14. P. Aninos, S. Oliveira, R. A. Matzner, Phys. Rev. 44, 1147 (1991)

    ADS  Google Scholar 

  15. D. K. Campbell, J. F. Schonfeld, C. A. Wingate, Physica D 9, 1 (1983)

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

    Google Scholar 

  17. R. H. Goodman, R. Haberman, SIAM J. Appl. Dyn. Syst. 4, 1195 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  18. R. H. Goodman, R. Haberman, Phys. Rev. Lett. 98, 105103 (2007)

    Article  ADS  Google Scholar 

  19. T. Sugiyama, Prog. Theor. Phys. 61, 1550 (1979)

    Article  ADS  Google Scholar 

  20. T. Romanczukiewicz, Ya. Shnir, Phys. Rev. Lett. 105, 081601 (2010)

    Article  ADS  Google Scholar 

  21. Ya. Shnir, Phys. Part. Nuclei Lett. 9, 745 (2012)

    Article  ADS  Google Scholar 

Download references

Funding

T. S. Mendonça received financial support from the Brazilian agency Coordenacao de Aperfeiçoamento de Pessoal de Nível Superior (CAPES); H. P. de Oliveira from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) (Grant No. E-26/202.998/518 2016 Bolsas de Bancada de Projetos (BBP)).

Author information

Authors and Affiliations

  1. Departamento de Física Teórica - Instituto de Física A. D. Tavares, Universidade do Estado do Rio de Janeiro, R. São Francisco Xavier, 524, Rio de Janeiro, RJ, 20550-013, Brazil

    T. S. Mendonça & H. P. de Oliveira

Authors
  1. T. S. Mendonça
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. P. de Oliveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. P. de Oliveira.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mendonça, T.S., de Oliveira, H. The Collision of Two-Kinks Revisited: the Creation of Kinks and Lump-Like Defects as Metastable States. Braz J Phys 49, 914–922 (2019). https://doi.org/10.1007/s13538-019-00703-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-019-00703-3

Keywords

Search

Navigation