Brazilian Journal of Physics

, Volume 48, Issue 6, pp 576–584 | Cite as

Multisoliton Dynamics in the Sine-Gordon Model with Two Point Impurities

  • Evgeniy G. EkomasovEmail author
  • Azamat M. Gumerov
  • Roman V. Kudryavtsev
  • Sergey V. Dmitriev
  • Vladimir N. Nazarov
Condensed Matter


Collective variables method is used to derive a set of differential equations to describe the dynamics of a kink in the sine-Gordon model with two identical point impurities taking damping into account. It is shown that the scenarios of kink interaction with the waves localized on the impurities, found from the reduced model, are similar to those obtained earlier by numerical integration of the continuous sine-Gordon equation. For the case of the kink passage through the region with the impurities, the structure and properties of the arising on impurities long-lived four-kink multisolitons are analyzed. For the approximate analytical description of the two bound impurity-localized nonlinear waves, the system of differential equations for harmonic oscillators with elastic link is obtained. The analytical model qualitatively reproduces the results of the sine-Gordon equation numerical simulation. The cases of large and small distances between impurities are analyzed. The results of our study uncover new features of the kink-impurity interaction which is important for a number of applications where the sine-Gordon model is used.


Kink Soliton Multisoliton Sine-Gordon equation Impurity Perturbation Collective variables 



The work was supported by Act 211 Government of the Russian Federation, contract № 02.A03.21.0011. For S.V.D., the work was supported by the Russian Science Foundation, grant No. 16-12-10175. The work was partly supported by the State Assignment of IMSP RAS. For A.M.G. and R.V.K., the work was supported by the Russian Foundation for Basic Research, grant No. 18-31-00122.


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Copyright information

© Sociedade Brasileira de Física 2018

Authors and Affiliations

  • Evgeniy G. Ekomasov
    • 1
    • 2
    Email author
  • Azamat M. Gumerov
    • 1
  • Roman V. Kudryavtsev
    • 1
    • 3
  • Sergey V. Dmitriev
    • 4
    • 5
  • Vladimir N. Nazarov
    • 3
  1. 1.Bashkir State UniversityUfaRussia
  2. 2.National Research South Ural State UniversityChelyabinskRussia
  3. 3.Subdivision of the Ufa Federal Research Centre of the Russian Academy of SciencesInstitute of Molecule and Crystal PhysicsUfaRussia
  4. 4.Institute for Metals Superplasticity Problems of the Russian Academy of SciencesUfaRussia
  5. 5.National Research Tomsk State UniversityTomskRussia

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