Skip to main content
SpringerLink
Log in

Interacting Localized Solutions of the Nonlinear Klein—Gordon Equation with a Variable Mass

  • Methods of Theoretical Physics
  • Published:
JETP Letters Aims and scope Submit manuscript

Abstract

A system consisting of material particles and a field is studied. The latter is described by the nonlinear Klein—Gordon equation. A modified Klein—Gordon equation, which allows the solutions of the Klein—Gordon equation with both zero and nonzero masses, is considered. Particles give rise to field inhomogeneities and interact with the field. It is shown that stable oscillating localized solutions are possible in this model. The oscillating localized solutions in this system generate traveling waves, leading to the interaction of these solutions at large distances.

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. A. Hasegawa and M. Matsumoto, Optical Solitons in Fibers (Springer, Berlin, Heidelberg, 1990).

    Book  Google Scholar 

  2. N. Akhmediev and A. Ankiewicz, Dissipative Solitons, Vol. 661 of Lecture Notes in Physics (Springer, Berlin, Heidelberg, 2005).

    Book  Google Scholar 

  3. A. R. Bishop, J. A. Krumhansl, and S. E. Trullinger, Phys. D (Amsterdam, Neth.) 1, 1 (1980).

    Article  ADS  Google Scholar 

  4. V. A. Rubakov, Classical Theory of Gauge Fields (URSS, Moscow, 1999; Princeton Univ. Press, Princeton, 2002).

    MATH  Google Scholar 

  5. D. S. Gorbunov and V. A. Rubakov, Introduction to the Theory of the Early Universe: Hot Big Bang Theory (URSS, Moscow, 2008; World Scientific, Singapore, 2011).

    MATH  Google Scholar 

  6. G. E. Brown, Selected Papers, with Commentary, of Tony Hilton Royle Skyrme, World Scientific 20th Century Physics (World Scientific, Singapore, 1995).

    Google Scholar 

  7. S. R. Coleman, Phys. Rev. D 11, 2088 (1975).

    Article  ADS  Google Scholar 

  8. Encyclopedia of Nonlinear Science, Ed. by A. Scott (Routledge, New York, 2004).

    MATH  Google Scholar 

  9. X. Jiang, Z. Fan, Z. Chen, W. Pang, Y. Li, and B. Malomed, Phys. Rev. A 93, 023633 (2016).

    Article  ADS  Google Scholar 

  10. B. A. Malomed, Phys. J. Spec. Top. 225, 2507 (2016).

    Article  Google Scholar 

  11. G. Fodor, P. Forgacs, Z. Horvath, and A. Lukacs, Phys. Rev. D 78, 025003 (2008).

    Article  ADS  Google Scholar 

  12. J. Cuevas, P. G. Kevrekidis, B. A. Malomed, P. Dyke, and R. G. Hulet, New J. Phys. 15, 063006 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  13. E. G. Ekomasov and R. K. Salimov, JETP Lett. 102, 122 (2015).

    Article  ADS  Google Scholar 

  14. R. K. Salimov, JETP Lett. 109, 490 (2019).

    Article  ADS  Google Scholar 

  15. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, and H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1984).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bashkir State University, Ufa, 450076, Russia

    R. K. Salimov & E. G. Ekomasov

  2. University of Tyumen, Tyumen, 625003, Russia

    E. G. Ekomasov

  3. South Ural State University, Chelyabinsk, 454080, Russia

    E. G. Ekomasov

Authors
  1. R. K. Salimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. G. Ekomasov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. K. Salimov.

Additional information

Russian Text © The Author(s), 2020, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 111, No. 3, pp. 209–212.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Salimov, R.K., Ekomasov, E.G. Interacting Localized Solutions of the Nonlinear Klein—Gordon Equation with a Variable Mass. Jetp Lett. 111, 193–195 (2020). https://doi.org/10.1134/S002136402003011X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S002136402003011X

Search

Navigation