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Influence of Transverse Perturbations on Breathers of the Sine-Gordon Equation

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Abstract

Based on a modification of the method of the average Lagrangian, the influence of transverse perturbations on the breather of the sine-Gordon equation is investigated using the procedure of double averaging over the phase and group canonical variables. It is demonstrated that the transverse perturbations on the eikonal stage promote self-focusing of breathers. A criterion for determining conditions of suppression of self-focusing effect by diffraction is obtained. The breathers containing an arbitrary number of phase oscillations are examined.

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REFERENCES

  1. V. G. Makhankov, C. Kummer, and A. B. Shvachka, Phys. Scripta, 20, 451-461 (1979).

    Google Scholar 

  2. R. Dodd, J. Ailback, J. Gibbon, and C. Morriob, Solitons and Nonlinear Wave Equations [Russian translation], Mir, Moscow (1988).

    Google Scholar 

  3. S. K. Zhdanov and B. A. Trubnikov, Quasi-Gaseous Unstable Media [in Russian], Nauka, Moscow (1991).

    Google Scholar 

  4. V. G. Makhan'kov, Yu. P. Rybakov, and V. I. Sanyuk, Usp. Fiz. Nauk, 164, No. 2, 121-147 (1994).

    Google Scholar 

  5. Frontiers of nonlinear physics. Progress in nonlinear science. Vol. II. Proc. Int. Conf. Dedicated to the 100thAnniversary of A. A. Andronov, Nizhnii Novgorod (2002).

  6. G. Whitham, Linear and Nonlinear Waves [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  7. S. V. Nesterov and S. V. Sazonov, Kvant. Elektron., 33, No. 2 (2004).

  8. T. Skyrme, Proc. R. Soc. London, A247, 260-278 (1958).

    Google Scholar 

  9. É. M. Belenov and A. V. Nazarkin, Pis'ma Zh. Eksp. Teor. Fiz., 51, 252-255 (1990).

    Google Scholar 

  10. S. V. Nesterov and S. V. Sazonov, Fiz. Tverd. Tela, 45, 303-308 (2003).

    Google Scholar 

  11. S. V. Sazonov, Zh. Eksp. Teor. Fiz., 119, 419-433 (2001).

    Google Scholar 

  12. R. Mattuck, A Guide to Feynman Diagrams in the Many-Body Problem [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  13. S. V. Sazonov, Usp. Fiz. Nauk, 171, 663-677 (2001).

    Google Scholar 

  14. S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses [in Russian], Nauka, Moscow (1988).

    Google Scholar 

  15. N. V. Karlovg and N. A. Kirichenko, Oscillations, Waves, and Structures [in Russian], Fizmatlit, Moscow (2001).

    Google Scholar 

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Authors and Affiliations

  1. Kaliningrad State University, Russia

    S. V. Nesterov & S. V. Sazonov

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  1. S. V. Nesterov
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  2. S. V. Sazonov
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Nesterov, S.V., Sazonov, S.V. Influence of Transverse Perturbations on Breathers of the Sine-Gordon Equation. Russian Physics Journal 47, 517–524 (2004). https://doi.org/10.1023/B:RUPJ.0000046325.14723.c3

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  • DOI: https://doi.org/10.1023/B:RUPJ.0000046325.14723.c3

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