Skip to main content
SpringerLink
Log in

Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of N slow kinks in the sine-Gordon model were calculated analytically (for N = 1, 2, and 3) and numerically (for 4 ≤ N ≤ 7). However, for many physical applications it is important to know not only the total potential energy density but also its two components (the on-site potential energy density and the elastic strain energy density) as well as the extreme values of the elastic strain, tensile (positive) and compressive (negative). In the present study we give (i) the two components of the potential energy density and (ii) the extreme values of elastic strain. Our results suggest that in multi-soliton collisions the main contribution to the potential energy density comes from the elastic strain, but not from the on-site potential. It is also found that tensile strain is usually larger than compressive strain in the core of multi-soliton collision.

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

Similar content being viewed by others

References

  1. Yu.S. Kivshar, G.P. Agrawal, Optical solitons from fibers to photonic crystals (Academic Press, Burlington, 2003)

  2. S.V. Suchkov, A.A. Sukhorukov, J. Huang, S.V. Dmitriev, C. Lee, Yu.S. Kivshar, Laser Photonics Rev. 10, 177 (2016)

    Article  Google Scholar 

  3. P.S. Lomdahl, J. Stat. Phys. 39, 551 (1985)

    Article  ADS  Google Scholar 

  4. J. Pfeiffer, M. Schuster, A.A. Abdumalikov, A.V. Ustinov, Phys. Rev. Lett. 96, 034103 (2006)

    Article  ADS  Google Scholar 

  5. S. Watanabe, H.S.J. van der Zant, S.H. Strogatz, T.P. Orlando, Physica D 97, 429 (1996)

    Article  ADS  Google Scholar 

  6. N. Manton, P. Sutcliffe, Topological solitons (Cambridge University Press, Cambridge, UK, 2004)

  7. H. Weigel, Chiral soliton models for baryons, Lect. Notes Phys. (Springer, Berlin, 2008), Vol. 743

  8. A.R. Bishop, T. Schneider editors, Solitons in condensed matter physics (Springer Verlag, Berlin, 1978)

  9. R.N. Garifullin, L.A. Kalyakin, M.A. Shamsutdinov, Comput. Math. Math. Phys. 47, 1158 (2007)

    Article  MathSciNet  Google Scholar 

  10. S.V. Dmitriev, K. Abe, T. Shigenari, Phys. Rev. B 58, 2513 (1998)

    Article  ADS  Google Scholar 

  11. S.V. Dmitriev, T. Shigenari, A.A. Vasiliev, K. Abe, Phys. Rev. B 55, 8155 (1997)

    Article  ADS  Google Scholar 

  12. S.V. Dmitriev, K. Abe, T. Shigenari, J. Phys. Soc. Jpn. 65, 3938 (1996)

    Article  ADS  Google Scholar 

  13. F.J. Buijnsters, A. Fasolino, M.I. Katsnelson, Phys. Rev. Lett. 113, 217202 (2014)

    Article  ADS  Google Scholar 

  14. E.A. Korznikova, S.V. Dmitriev, J. Phys. D: Appl. Phys. 47, 345307 (2014)

    Article  Google Scholar 

  15. R.D. Yamaletdinov, V.A. Slipko, Y.V. Pershin, Phys. Rev. B 96, 094306 (2017)

    Article  ADS  Google Scholar 

  16. T.I. Belova, A.E. Kudryavtsev, Phys. Usp. 40, 359 (1997)

    Article  ADS  Google Scholar 

  17. O.M. Braun, Yu.S. Kivshar, The Frenkel-Kontorova model: concepts, methods, and applications (Springer, Berlin, 2004)

  18. J. Cuevas-Maraver, P.G. Kevrekidis, F. Williams editors, The sine-Gordon model and its applications from pendula and Josephson junctions to gravity and high energy physics (Springer, Berlin, 2014)

  19. S.Y. Lou, H.C. Hu, X.Y. Tang, Phys. Rev. E 71, 036604 (2005)

    Article  ADS  Google Scholar 

  20. J.K. Perring, T.H.R. Skyrme, Nucl. Phys. 31, 550 (1962)

    Article  Google Scholar 

  21. R. Hirota, J. Phys. Soc. Jpn. 33, 1459 (1972)

    Article  ADS  Google Scholar 

  22. P.J. Caudrey, J.C. Eilbeck, J.D. Gibbon, R.K. Bullough, J. Phys. A: Math. Nucl. Gen. 6, L112 (1973)

    Article  ADS  Google Scholar 

  23. V.A. Gani, A.E. Kudryavtsev, Phys. Rev. E 60, 3305 (1999)

    Article  ADS  Google Scholar 

  24. A.M. Wazwaz, J. Appl. Math. Inf. 30, 925 (2012)

    Google Scholar 

  25. A.M. Gumerov, E.G. Ekomasov, F.K. Zakir’yanov, R.V. Kudryavtsev, Comput. Math. Math. Phys. 54, 491 (2014)

    Article  MathSciNet  Google Scholar 

  26. A.M. Gumerov, E.G. Ekomasov, R.R. Murtazin, V.N. Nazarov, Comput. Math. Math. Phys. 55, 628 (2015)

    Article  MathSciNet  Google Scholar 

  27. V.A. Gani, V. Lensky, M.A. Lizunova, J. High Energy Phys. 08, 147 (2015)

    Article  Google Scholar 

  28. S.V. Dmitriev, P.G. Kevrekidis, Yu.S. Kivshar, Phys. Rev. E 78, 046604 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  29. S.V. Dmitriev, Yu.S. Kivshar, T. Shigenari, Phys. Rev. E 64, 056613 (2001)

    Article  ADS  Google Scholar 

  30. A.E. Miroshnichenko, S.V. Dmitriev, A.A. Vasiliev, T. Shigenari, Nonlinearity 13, 837 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  31. K. Javidan, J. Phys. A 39, 10565 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  32. D. Saadatmand, S.V. Dmitriev, P.G. Kevrekidis, Phys. Rev. D 92, 056005 (2015)

    Article  ADS  Google Scholar 

  33. A. Moradi Marjaneh, D. Saadatmand, K. Zhou, S.V. Dmitriev, M.E. Zomorrodian, Commun. Nonlinear Sci. 49, 30 (2017)

    Article  Google Scholar 

  34. A. Moradi Marjaneh, V.A. Gani, D. Saadatmand, S.V. Dmitriev, K. Javidan, J. High Energy Phys. 07, 028 (2017)

    Article  ADS  Google Scholar 

  35. R. Rajaraman, Phys. Rep. 21, 227 (1975)

    Article  ADS  Google Scholar 

  36. Yu.S. Kivshar, D.E. Pelinovsky, T. Cretegny, M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998)

    Article  ADS  Google Scholar 

  37. N.R. Quintero, A. Sanchez, F.G. Mertens, Phys. Rev. E 62, 5695 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  38. V.A. Gani, A.E. Kudryavtsev, M.A. Lizunova, Phys. Rev. D 89, 125009 (2014)

    Article  ADS  Google Scholar 

  39. P. Dorey, K. Mersh, T. Romanczukiewicz, Y. Shnir, Phys. Rev. Lett. 107, 091602 (2011)

    Article  ADS  Google Scholar 

  40. V.A. Gani, M.A. Lizunova, R.V. Radomskiy, J. High Energy Phys. 4, 43 (2016)

    ADS  Google Scholar 

  41. A. Khare, I.C. Christov, A. Saxena, Phys. Rev. E 90, 023208 (2014)

    Article  ADS  Google Scholar 

  42. A.E. Kudryavtsev, M.A. Lizunova, Phys. Rev. D 95, 056009 (2017)

    Article  ADS  Google Scholar 

  43. K. Javidan, Phys. Rev. E 78, 046607 (2008)

    Article  ADS  Google Scholar 

  44. Ya. Frenkel, T. Kontorova, Phys. Z. Sowjetunion 13, 1 (1938)

    Google Scholar 

  45. B. Ahn, A.P. Zhilyaev, H.-J. Lee, M. Kawasaki, T.G. Langdon, Mater. Sci. Eng. A 635, 109 (2015)

    Article  Google Scholar 

  46. C.M. Cepeda-Jimenez, J.I. Beltran, A. Hernando, M.A. Garcia, F. Yndurain, A. Zhilyaev, M.T. Perez-Prado, Acta Mater. 123, 206 (2017)

    Article  Google Scholar 

  47. W.H. Li, X.H. Yao, P.S. Branicio, X.Q. Zhang, N.B. Zhang, Acta Mater. 140, 274 (2017)

    Article  Google Scholar 

  48. S.V. Dmitriev, T. Shigenari, Chaos 12, 324 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  49. S.V. Dmitriev, P.G. Kevrekidis, B.A. Malomed, D.J. Frantzeskakis, Phys. Rev. E 68, 056603 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  50. S.V. Dmitriev, P.G. Kevrekidis, N. Yoshikawa, J. Phys. A: Math. Gen. 38, 7617 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Quchan Branch, Islamic Azad University, Quchan, Iran

    Aliakbar Moradi Marjaneh

  2. Department of Physics, Ferdowsi University of Mashhad, 91775-1436, Mashhad, Iran

    Alidad Askari

  3. Department of Physics, University of Sistan and Baluchestan, Zahedan, Iran

    Danial Saadatmand

  4. Institute for Metals Superplasticity Problems RAS, Khalturin Street 39, 450001, Ufa, Russia

    Sergey V. Dmitriev

  5. National Research Tomsk State University, Lenin Ave. 36, 634050, Tomsk, Russia

    Sergey V. Dmitriev

Authors
  1. Aliakbar Moradi Marjaneh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alidad Askari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Danial Saadatmand
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sergey V. Dmitriev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Aliakbar Moradi Marjaneh.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Marjaneh, A.M., Askari, A., Saadatmand, D. et al. Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions. Eur. Phys. J. B 91, 22 (2018). https://doi.org/10.1140/epjb/e2017-80406-y

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2017-80406-y

Keywords

Search

Navigation