Generation of wave packets and breathers by oscillating kinks in the sine-Gordon system

Evolution of the nonequilibrium inhomogeneities and topological defects is studied in terms of complex kink solutions of the sine-Gordon equation. The weakly damped oscillation of the sine-Gordon kink, named as the kink quasimode, is described explicitly. It is shown that the oscillatory kink behavior and the wave packet generation depend significantly on the initial nonequilibrium kink profile. In order to specify conditions of the generationof wobbling kinks with a multibreather structure we reformulate the direct scattering problem associated with the sine-Gordon equation as the spectral problem of the Schrödinger operator. We obtain the dependence of the radiation energy, which is emitted during formation of the multi-frequency wobbling kink, on the effective dimension of its initial profile.

Key words: nonlinear dynamics, sine-Gordon equation, quasimode, wobbling kink, radiation.

References

1. S. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Theory of Solitons: The Inverse Scattering Method (Springer US, New York 1984). Google Scholar

2. O. V. Charkina and M. M. Bogdan, Symmetry, Integrability Geom.: Methods Appl. 2, 047 (2006). CrossRef Google Scholar

3. H. Segur, J. Math. Phys. 24, 1439 (1983). CrossRef Google Scholar

4. G. Kalbermann, J. Phys. A. 37, 11603 (2004). CrossRef Google Scholar

5. R. Boesch and C. R. Willis, Phys. Rev. B 42, 2290 (1990). CrossRef Google Scholar

6. N. R. Quintero, A. Sanchez, and F. G. Mertens, Phys. Rev. E 62, 60 (2000). CrossRef Google Scholar

7. M. J. Rice, Phys. Rev. B 28, 3587 (1983). CrossRef Google Scholar

8. N. F. Smyth and A. L. Worthy, Phys. Rev. E 60, 2330 (1999). CrossRef Google Scholar

9. E. Majernikova, Y. B. Gaididei, and O. M. Braun, Phys. Rev. E 52, 1241 (1995). CrossRef Google Scholar

10. J. A. Gonzalez, A. BellorÄ±n, and L. E. Guerrero, Phys. Rev. E 65, 065601 (2002). CrossRef Google Scholar

11. D. K. Campbell, J. F. Schonfeld, and C. A. Wingate, Physica D 9, 1 (1983). CrossRef Google Scholar

12. D. K. Campbell, M. Peyrard, and P. Sodano, Physica D 19, 165 (1986). CrossRef Google Scholar

13. J. Frenkel and T. Kontorova, Phys. Z. Sowietunion 13, 1 (1938). Google Scholar

14. M. M. Bogdan and O. V. Charkina, Fiz. Nizk. Temp. 34, 713 (2008) [Low Temp. Phys. 34, 564 (2008)]. CrossRef Google Scholar

15. M. M. Bogdan and A. M. Kosevich, Proc. Estonian Acad. Sci. Phys. Math. 46, 14 (1997). CrossRef Google Scholar

16. M. M. Bogdan, A. M. Kosevich, and G. A. Maugin, Cond. Matt. Phys. 2, 255 (1999). CrossRef Google Scholar

17. M. M. Bogdan, A. M. Kosevich, and G. A. Maugin, Wave Motion 34, 1 (2001). CrossRef Google Scholar

18. P. G. Kevrekidis, I. G. Kevrekidis, A. R. Bishop, and E. S. Titi, Phys. Rev. E 65, 046613 (2002). CrossRef Google Scholar

19. S. R. Sharma and B. Bergersen, Phys. Rev. B 30, 6586 (1984). CrossRef Google Scholar

20. P. G. Kevrekidis and C. K. R. T. Jones, Phys. Rev. E 61, 3114 (2000). CrossRef Google Scholar

21. O. V. Charkina and M. M. Bogdan, Uzh. Univ. Sci. Herald. Series Physics. 17, 30 (2005) arXiv:2007.00984v1. CrossRef Google Scholar

22. N. S. Manton and H. Merabet, Nonlinearity 10, 3 (1997). CrossRef Google Scholar

23. I. V. Barashenkov and O. F. Oxtoby, Phys. Rev. E 80, 026608 (2009). CrossRef Google Scholar

24. L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1977). Google Scholar

25. R. Buckingham and P. D. Miller, Physica D 237, 2296 (2008). CrossRef Google Scholar

26. A. M. Kosevich and A. S. Kovalev, JETP 40, 891 (1975), available at http://www.jetp.ac.ru/cgi-bin/e/index/e/40/5/p891?a=list. CrossRef Google Scholar