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Nonlinear localization of excitations and the dynamics of solitons in self-modulated systems

  • Nonlinear Physics
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Abstract

The nonlinear dynamics of systems with a spatially periodic ground state was studied. The dynamics of kinks against the background of a periodic soliton structure was considered for the example of the sine-Klein-Gordon model that described a fluxon lattice in a long Josephson contact in an external magnetic field and an incommensurate structure of a surface atomic layer or adatom chains on the surface of a crystal. The velocity of moving kinks was shown to be bounded from above and from below if the ground state was spatially periodic.

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References

  1. D. L. Mills and J. Trullinger, Phys. Rev. B 36, 947 (1987).

    ADS  Google Scholar 

  2. O. A. Chubykalo, A. S. Kovalev, and O. V. Usatenko, Phys. Rev. B 47, 3153 (1993).

    ADS  Google Scholar 

  3. A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).

    Article  ADS  Google Scholar 

  4. R. A. Ferell and R. E. Prange, Phys. Rev. Lett. 40, 479 (1963).

    ADS  Google Scholar 

  5. D. J. Scalapino, in Tunneling Phenomena in Solids, Ed. by E. Burstein and S. Lundqvist (Plenum, New York, 1969), p. 477.

    Google Scholar 

  6. U. Harten, A. M. Lahee, J. P. Toennies, and Ch. Woll, Phys. Rev. Lett. 54, 2619 (1985).

    Article  ADS  Google Scholar 

  7. M. Mansfield and R. J. Needs, J. Phys.: Condens. Matter 2, 2361 (1990).

    Article  ADS  Google Scholar 

  8. O. Braun and Yu. S. Kivshar, Phys. Rep. 306, 4 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  9. V. G. Bar’yakhtar, T. K. Soboleva, and A. L. Sukstanskii, Fiz. Tverd. Tela (Leningrad) 27, 2428 (1985) [Sov. Phys. Solid State 27, 1454 (1985)].

    Google Scholar 

  10. E. P. Stefanovskii and A. L. Sukstanskii, Zh. Éksp. Teor. Fiz. 104, 3434 (1993) [JETP 77, 628 (1993)].

    Google Scholar 

  11. A. M. Kosevich and A. S. Kovalev, Introduction to the Nonlinear Physical Mechanics (Naukova Dumka, Kiev, 1989).

    Google Scholar 

  12. A. M. Kosevich, Theory of Crystal Lattice (Vishcha Shkola, Khar’kov, 1988).

    Google Scholar 

  13. I. O. Kulik and I. K. Yanson, in Josephson Effect in Superconducting Tunnel Structures (Nauka, Moscow, 1970).

    Google Scholar 

  14. P. Lebwohl and M. Stephen, Phys. Rev. 163, 376 (1967).

    Article  ADS  Google Scholar 

  15. E. T. Whittaker and G. N. Watson, Modern Analysis (Cambridge Univ. Press, New York, 1940), Chap. XXIII.

    Google Scholar 

  16. V. M. Eleonskii, N. E. Kulagin, and N. S. Novozhilova, Zh. Éksp. Teor. Fiz. 89, 2174 (1985) [Sov. Phys. JETP 62, 1255 (1985)].

    Google Scholar 

  17. V. M. Eleonskii and N. E. Kulagin, Fiz. Met. Metalloved. 65, 868 (1988).

    Google Scholar 

  18. A. S. Kovalev and N. E. Kulagin, Preprint No. 14-87, FTINT AN USSR (Khar’kov, 1987).

  19. M. A. Sall’, Teor. Mat. Fiz. 52, 227 (1982).

    MathSciNet  Google Scholar 

  20. A. S. Kovalev, A. D. Kondratyuk, and A. I. Landau, Preprint No. 26-89, FTINT AN USSR (Khar’kov, 1989).

  21. H. Toda, Prog. Theor. Phys. Suppl. 45, 174 (1970).

    Google Scholar 

  22. H. Toda, Prog. Theor. Phys. Suppl. 59, 1 (1976).

    Google Scholar 

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Authors and Affiliations

  1. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkov, 61103, Ukraine

    A. S. Kovalev

  2. Institute for Theoretical Physics, National Scientific Center Kharkov Institute of Physics and Technology, Kharkov, 61108, Ukraine

    I. V. Gerasimchuk

Authors
  1. A. S. Kovalev
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  2. I. V. Gerasimchuk
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Translated from Zhurnal Éksperimental’no\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) i Teoretichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 122, No. 5, 2002, pp. 1116–1124.

Original Russian Text Copyright © 2002 by Kovalev, Gerasimchuk.

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Kovalev, A.S., Gerasimchuk, I.V. Nonlinear localization of excitations and the dynamics of solitons in self-modulated systems. J. Exp. Theor. Phys. 95, 965–972 (2002). https://doi.org/10.1134/1.1528689

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  • DOI: https://doi.org/10.1134/1.1528689

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