Journal of Physical Studies 23(3), Article 3001 [3 pages] (2019)
DOI: https://doi.org/10.30970/jps.23.3001

KINK SOLUTIONS FOR THE NEWELL--WHITEHEAD--SEGEL EQUATION

M. A. Knyazev

Belarusian National Technical University,
65, Independence Ave., Minsk, 220013, Belarus
e-mail: maknyazev@bntu.by

Four kink (antikink) solutions for the Newell-Whitehead-Segel equation are constructed by the Hirota method for the special but general enough values of its parameters. The topological charges for these solutions are calculated. A possibility of the spontaneous symmetry breaking is pointed out.

PACS number(s): 02.30.Jr, 03.50.Kk

pdf

References
  1. A. Newell, J. Whitehead, J. Fluid Mechan. 38, 279 (1969);
    CrossRef
  2. L. A. Segel, J. Fluid Mechan. 38, 203 (1969);
    CrossRef
  3. J. D. Murray: Mathematical Biology I: An Introduction (Spinger, New York, 2002).
  4. R. Graham, Phys. Rev. Lett. 76, 2185 (1996);
    CrossRef ;
  5. erratum: Phys. Rev. Lett. 80, 3888 (1998);
    CrossRef
  6. B. A. Malomed, preprint arXiv:patt-sol/9605001 (1996).
  7. S. S. Nourazar, M. Soori, A. Nazari-Golshan, Aust. J. Basic Appl. Sci. 5, 1400 (2011).
  8. A. A. Aswhad, A. F. Jaddoa, Al-Mustansiriyah J. Sci. 25, 45 (2014);
    CrossRef
  9. A. Saravanan, N. Magesh, J. Egypt Math. Society 21, 259 (2013);
    CrossRef
  10. A. Prakash, M. Kumar, J. Appl. Anal. Comput. 6, 738 (2016);
    CrossRef
  11. G. O. Akinlabi, S. O. Edek, J. Math. Stat. 13, 24 (2017);
    CrossRef
  12. O. Vaneeva, V. Boyko, A. Zhalji, C. Sophocleous, J. Math. Anal. Appl. 474, 264 (2019);
    CrossRef
  13. M. J. Ablowitz, H. Segur, Solitons and Inverse Scattering Transform (SIAM, Philadelphia, 1981).
  14. E. Infeld, G. Rowlands: Nonlinear Waves, Solitons and Chaos (Cambridge University Press, 2000).
  15. J. M. Cervero, P. G. Est\'evez, Phys. Lett. A 114, 435 (1986);
    CrossRef
  16. R. Rajaraman, Solitons and Instantons {North-Holland Publ. Co., 1982}.
  17. M. A. Knyazev, Kinks in the Scalar Model with Damping (Tekhnologia, Minsk, 2003) [in Russian].