Skip to main content
SpringerLink
Log in

Influence of dislocations on kink solutions of the double sine-Gordon equation

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

Dependences related to the formation of kinks and their interaction with local perturbations defined as a smooth function of coordinates multiplying the sine of complete argument in the double sine-Gordon equation are studied. It is shown that there are nonstationary kink solutions remaining within the perturbation domain. These solutions consist of two separate 2π-kinks oscillating about the center of the perturbation. The interactions of these kinks with 4π-kinks have a complicated character depending not only on the velocity but also on the phases of the kink pairs. The transmission, capture, and reflection of kinks are investigated. The computations were based on the quasispectral Fourier method and the fourth-order Runge-Kutta method.

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. V. G. Makhan’kov, “Solitons and numerical experiment,” Sov. J. Part. Nucl. 14, 50–75 (1983).

    MathSciNet  Google Scholar 

  2. T. I. Belova and A. E. Kudryavtsev, “Solitons and their interactions with classical field theory,” Usp. Fiz. Nauk 167, 377–406 (1997).

    Article  Google Scholar 

  3. V. A. Gani and A. E. Kudryavtsev, “Kink-antikink interaction in the double sine-Gordon equation and the problem of resonance frequencies,” Phys. Rev. E 60Part 3, 3305–3309 (1999).

    Article  Google Scholar 

  4. S. W. Goatham, L. E. Mannering, R. Hann, and S. Krusch, “Dynamics of multi-kinks in the presence of wells and barriers,” Acta Phys. Pol. A 42, 2087–2106 (2011).

    Google Scholar 

  5. G. Kalbermann, “The sine-Gordon wobble,” J. Phys. A: Math. Gen. 37, 11603–11612 (2004).

    Article  MathSciNet  Google Scholar 

  6. Y. R. Kivshar and B. A. Malomed, “Radiative and inelastic effects in dynamics of double sine-Gordon solitons,” Phys. Lett. A 122, 245–248 (1987).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    S. P. Popov

Authors
  1. S. P. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. P. Popov.

Additional information

Original Russian Text © S.P. Popov, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 12, pp. 2072–2081.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popov, S.P. Influence of dislocations on kink solutions of the double sine-Gordon equation. Comput. Math. and Math. Phys. 53, 1891–1899 (2013). https://doi.org/10.1134/S0965542513120099

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542513120099

Keywords

Search

Navigation