Scattering of compact oscillons

Abstract

We study various aspects of the scattering of generalized compact oscillons in the signum-Gordon model in (1+1) dimensions. Using covariance of the model we construct traveling oscillons and study their interactions and the dependence of these interactions on the oscillons’ initial velocities and their relative phases. The scattering processes transform the two incoming oscillons into two outgoing ones and lead to the generation of extra oscillons which appear in the form of jet-like cascades. Such cascades vanish for some values of free parameters and the scattering processes, even though our model is non-integrable, resemble typical scattering processes normally observed for integrable or quasi-integrable models.

Occasionally, in the intermediate stage of the process, we have seen the emission of shock waves and we have noticed that, in general, outgoing oscillons have been more involved in their emission than the initial ones i.e. they have a border in the form of curved worldlines.

The results of our studies of the scattering of oscillons suggest that the radiation of the signum-Gordon model has a fractal-like nature.

A preprint version of the article is available at ArXiv.

References

  1. [1]

    I.L. Bogolyubsky and V.G. Makhankov, Lifetime of Pulsating Solitons in Some Classical Models, Pisma Zh. Eksp. Teor. Fiz.24 (1976) 15 [INSPIRE].

    Google Scholar 

  2. [2]

    M. Gleiser, Pseudostable bubbles, Phys. Rev.D 49 (1994) 2978 [hep-ph/9308279] [INSPIRE].

  3. [3]

    M. Gleiser, Oscillons in scalar field theories: Applications in higher dimensions and inflation, Int. J. Mod. Phys.D 16 (2007) 219 [hep-th/0602187] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  4. [4]

    M. Gleiser and M. Krackow, Resonant configurations in scalar field theories: Can some oscillons live forever?, Phys. Rev.D 100 (2019) 116005 [arXiv:1906.04070] [INSPIRE].

    ADS  Google Scholar 

  5. [5]

    Y.M. Shnir, Topological and Non-Topological Solitons in Scalar Field Theories, Cambridge University Press, Cambridge U.K. (2018).

    Google Scholar 

  6. [6]

    P. Salmi and M. Hindmarsh, Radiation and Relaxation of Oscillons, Phys. Rev.D 85 (2012) 085033 [arXiv:1201.1934] [INSPIRE].

  7. [7]

    G. Fodor, P. Forgacs, P. Grandclement and I. Racz, Oscillons and Quasi-breathers in the φ 4Klein-Gordon model, Phys. Rev.D 74 (2006) 124003 [hep-th/0609023] [INSPIRE].

    ADS  Google Scholar 

  8. [8]

    G. Fodor, P. Forgacs, Z. Horvath and A. Lukács, Small amplitude quasi-breathers and oscillons, Phys. Rev.D 78 (2008) 025003 [arXiv:0802.3525] [INSPIRE].

  9. [9]

    T. Románczukiewicz and Y.M. Shnir, Oscillon resonances and creation of kinks in particle collisions, Phys. Rev. Lett.105 (2010) 081601 [arXiv:1002.4484] [INSPIRE].

  10. [10]

    T. Romańczukiewicz and Y.M. Shnir, Oscillons in the presence of external potential, JHEP01 (2018) 101 [arXiv:1706.09234] [INSPIRE].

  11. [11]

    R.A.C. Correa, W. de Paula, T. Frederico, O. Oliveira and F.E.M. Silveira, Oscillons in ϕ 6-theories: Possible occurrence in MHD, arXiv:1806.04412 [INSPIRE].

  12. [12]

    R.A.C. Correa, A. de Souza Dutra, T. Frederico, B.A. Malomed, O. Oliveira and N. Sawado, Creating Oscillons and Oscillating Kinks in Two Scalar Field Theories, arXiv:1907.07145 [INSPIRE].

  13. [13]

    J. Sakstein and M. Trodden, Oscillons in Higher-Derivative Effective Field Theories, Phys. Rev.D 98 (2018) 123512 [arXiv:1809.07724] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  14. [14]

    C. Adam, T. Románczukiewicz and A. Wereszczyński, The ϕ 4model with the BPS preserving defect, JHEP03 (2019) 131 [arXiv:1812.04007] [INSPIRE].

  15. [15]

    T. Románczukiewicz and Y.M. Shnir, Some Recent Developments on Kink Collisions and Related Topics, in A dynamical perspective on the ϕ 4model, Nonlinear Systems and Complexity Series, volume 26, P. Kevrekidis and J. Cuevas-Maraver eds., Springer, Cham Switzerland (2019) [arXiv:1809.04896] [INSPIRE].

  16. [16]

    D. Bazeia, E. Belendryasova and V.A. Gani, Scattering of kinks in a non-polynomial model, J. Phys. Conf. Ser.934 (2017) 012032 [arXiv:1711.07788] [INSPIRE].

    Google Scholar 

  17. [17]

    A. Alonso-Izquierdo, Kink dynamics in the MSTB model, Phys. Scripta94 (2019) 085302 [arXiv:1804.05605] [INSPIRE].

  18. [18]

    M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, Method for solving the Sine-Gordon equation, Phys. Rev. Lett.30 (1973) 1262 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  19. [19]

    M.J. Ablowitz, D.J. Kaup, A.C. Newell and H. Segur, Nonlinear-Evolution Equations of Physical Significance, Phys. Rev. Lett.31 (1973) 125 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  20. [20]

    L.A. Ferreira and W.J. Zakrzewski, A Simple formula for the conserved charges of soliton theories, JHEP09 (2007) 015 [arXiv:0707.1603] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. [21]

    D.I. Olive, N. Turok and J.W.R. Underwood, Affine Toda solitons and vertex operators, Nucl. Phys.B 409 (1993) 509 [hep-th/9305160] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  22. [22]

    M. Tajiri and Y. Watanabe, Breather solutions to the focusing nonlinear Schrodinger equation, Phys. Rev.E 57 (1998) 3510.

    ADS  MathSciNet  Google Scholar 

  23. [23]

    D.J. Kedziora, A. Ankiewicz and N. Akhmediev, Second-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits, Phys. Rev.E 85 (2012) 066601.

  24. [24]

    H. Arodź, P. Klimas and T. Tyranowski, Compact oscillons in the signum-Gordon model, Phys. Rev.D 77 (2008) 047701 [arXiv:0710.2244] [INSPIRE].

  25. [25]

    H. Arodź and Z. Świerczyński, Swaying oscillons in the signum-Gordon model, Phys. Rev.D 84 (2011) 067701 [arXiv:1106.3169] [INSPIRE].

  26. [26]

    Z. Świerczyński, On the oscillons in the signum-Gordon model, J. Nonlin. Math. Phys.24 (2017) 20 [INSPIRE].

  27. [27]

    H. Arodź, P. Klimas and T. Tyranowski, Field-theoretic models with V-shaped potentials, Acta Phys. Polon.B 36 (2005) 3861 [hep-th/0510204] [INSPIRE].

  28. [28]

    H. Arodź, Topological compactons, Acta Phys. Polon.B 33 (2002) 1241 [nlin/0201001] [INSPIRE].

  29. [29]

    D. Bazeia, L. Losano, M.A. Marques, R. Menezes and R. da Rocha, Compact Q-balls, Phys. Lett.B 758 (2016) 146 [arXiv:1604.08871] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  30. [30]

    D. Bazeia, M.A. Marques and R. Menezes, Compact Lumps, Europhys. Lett.111 (2015) 61002 [arXiv:1509.06634] [INSPIRE].

    ADS  Article  Google Scholar 

  31. [31]

    D. Bazeia, L. Losano, M.A. Marques and R. Menezes, Compact Structures in Standard Field Theory, Europhys. Lett.107 (2014) 61001 [arXiv:1404.2493] [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    D. Bazeia, L. Losano, M.A. Marques and R. Menezes, Compact Chern-Simons vortices, Phys. Lett.B 772 (2017) 253 [arXiv:1706.00969] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  33. [33]

    D. Bazeia, E. da Hora and D. Rubiera-Garcia, Compact vortex in a generalized Born-Infeld model, Phys. Rev.D 84 (2011) 125005 [arXiv:1103.4940] [INSPIRE].

    ADS  Google Scholar 

  34. [34]

    H. Arodź, P. Klimas and T. Tyranowski, Scaling, self-similar solutions and shock waves for V-shaped field potentials, Phys. Rev.E 73 (2006) 046609 [hep-th/0511022] [INSPIRE].

  35. [35]

    C. Adam, D. Foster, S. Krusch and A. Wereszczyński, BPS sectors of the Skyrme model and their non-BPS extensions, Phys. Rev.D 97 (2018) 036002 [arXiv:1709.06583] [INSPIRE].

  36. [36]

    C. Adam, P. Klimas, J. Sanchez-Guillen and A. Wereszczyński, Compact baby skyrmions, Phys. Rev.D 80 (2009) 105013 [arXiv:0909.2505] [INSPIRE].

  37. [37]

    P. Klimas, J.S. Streibel, A. Wereszczyński and W.J. Zakrzewski, Oscillons in a perturbed signum-Gordon model, JHEP04 (2018) 102 [arXiv:1801.05454] [INSPIRE].

  38. [38]

    P. Klimas and L.R. Livramento, Compact Q-balls and Q-shells in CPN type models, Phys. Rev.D 96 (2017) 016001 [arXiv:1704.01132] [INSPIRE].

  39. [39]

    C. Adam, J. Sanchez-Guillen and A. Wereszczyński, A Skyrme-type proposal for baryonic matter, Phys. Lett.B 691 (2010) 105 [arXiv:1001.4544] [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    F.M. Hahne, P. Klimas and J.S. Streibel, On decay of shock-like waves into compact oscillons, arXiv:1909.11137 [INSPIRE].

  41. [41]

    J. Brand, B. Piette and W.J. Zakrzewski, Scattering of topological solitons on holes and barriers, J. Phys.A 38 (2005) 10403 [hep-th/0508032] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  42. [42]

    B. Piette and W.J. Zakrzewski, Dynamical properties of a soliton in a potential well, J. Phys.A 40 (2007) 329 [hep-th/0610095] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  43. [43]

    L.A. Ferreira and W.J. Zakrzewski, Breather-like structures in modified sine-Gordon models, Nonlinearity29 (2016) 1622 [arXiv:1404.5812v1] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  44. [44]

    L.A. Ferreira and W.J. Zakrzewski, Numerical and analytical tests of quasi-integrability in modified sine-Gordon models, JHEP01 (2014) 058 [arXiv:1308.4412] [INSPIRE].

    ADS  Article  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

Author information

Affiliations

Authors

Corresponding author

Correspondence to P. Klimas.

Additional information

ArXiv ePrint: 1909.01992

CNPq Scholarship holder — Brazil. (F. M. Hahne)

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hahne, F.M., Klimas, P., Streibel, J.S. et al. Scattering of compact oscillons. J. High Energ. Phys. 2020, 6 (2020). https://doi.org/10.1007/JHEP01(2020)006

Download citation

Keywords

  • Solitons Monopoles and Instantons
  • Effective Field Theories
  • Integrable Field Theories