Abstract
We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation controlled by two parameters, one very small, used to control a linear expansion on it, and the other, which specifies the particular model in the family of models. We investigate the presence of topological defects, showing how the solutions can be constructed explicitly from the topological defects of the sine-Gordon model itself. In particular, we delve into the double sine-Gordon model in a braneworld scenario with a single extra dimension of infinite extent, showing that a stable gravity scenario is admissible. Also, we briefly show that the deformation procedure can be used iteratively, leading to a diversity of possibilities to construct families of models of the sine-Gordon type.
Similar content being viewed by others
References
R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdan, 1982)
A. Vilenkin, E.P.S. Shellard, Cosmig Strings and Others Topological Defects (Cambridge Univ. Press, Cambridge, 1994)
N. Manton, P. Sutcliffe, Topological Solitons (Cambridge Univ. Press, Cambridge, 2004)
D. Walgraef, Spatio-Temporal Pattern Formation (Springer, New York, 1997)
A. Vanhaverbeke, A. Bischof, R. Allenspach, Phys. Rev. Lett. 101, 107202 (2008)
G. Basar, G.V. Dunne, Phys. Rev. Lett. 100, 200404 (2008)
A. Alonso-Izquierdo, M.A. Gonzalez Leon, J. Mateos Guilarte, Phys. Rev. Lett. 101, 131602 (2008)
D. Bazeia, L. Losano, J.M.C. Malbouisson, Phys. Rev. D 66, 101701 (2002)
C.A. Almeida, D. Bazeia, L. Losano, J.M.C. Malbouisson, Phys. Rev. D 69, 067702 (2004)
V.I. Afonso, D. Bazeia, M.A. Gonzalez Leon, L. Losano, J. Mateos Guilarte, Nucl. Phys. B 810, 427 (2009)
D. Bazeia, A. Das, L. Losano, M.J. Santos, Appl. Math. Lett. 23, 681 (2010)
A. de Souza Dutra, Physica D 238, 798 (2009)
W.T. Cruz, M.O. Tahim, C.A.S. Almeida, Europhys. Lett. 88, 41001 (2009)
A.E.R. Chumbes, M.B. Hott, Phys. Rev. D 81, 045008 (2010)
R.R. Landim, G. Alencar, M.O. Tahim, R.N. Costa Filho, J. High Energy Phys. 1108, 071 (2011)
R. Landim, G. Alencar, M.O. Tahim, M.A.M. Gomes, R.N. Costa Filho, Europhys. Lett. 97, 20003 (2012)
A.E. Bernardini, R. da Rocha, Adv. High Energy Phys. 2013, 304980 (2013)
D. Bazeia, L. Losano, R. Menezes, M.M. Sousa, Europhys. Lett. 87, 21001 (2009)
G. Mussardo, V. Riva, G. Sotkov, Nucl. Phys. B 87, 548 (2005)
G. Mussardo, Nucl. Phys. B 779, 101 (2007)
A. Kundu, Phys. Rev. Lett. 99, 154101 (2007)
L. Benfatto, C. Castellani, T. Giamarchi, Phys. Rev. Lett. 99, 207002 (2007)
L.A. Ferreira, B. Piette, W.J. Zakrzewski, Phys. Rev. E 77, 036613 (2007)
M. Cadoni, Y.-X. Liu, L.-D. Zhang, L.-D. Zhang, Y.-S. Duan, Phys. Rev. D 78, 0650025 (2008)
D. Bazeia, L. Losano, J.M.C. Malbouisson, R. Menezes, Physica D 237, 937 (2008)
J.H. Al-Alawi, W.J. Zakrzewski, J. Phys. A 41, 315206 (2008)
L.A. Ferreira, W.J. Zakrzewski, J. High Energy Phys. 1105, 130 (2011)
L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999)
W.D. Goldberger, M.B. Wise, Phys. Rev. Lett. 83, 4922 (1999)
O. DeWolfe, D.Z. Freedman, S.S. Gubser, A. Karch, Phys. Rev. D 62, 046008 (2000)
M. Gremm, Phys. Lett. B 478, 434 (2000)
R. Koley, S. Kar, Class. Quantum Gravity 22, 753 (2005)
Y. Brihaye, T. Delsate, Phys. Rev. D 86, 024029 (2012)
E.B. Bogomol’nyi, Sov. J. Nucl. Phys. 24, 449 (1976)
M.K. Prasad, C.M. Sommerfield, Phys. Rev. Lett. 35, 760 (1975)
D. Bazeia, Phys. Rev. D 60, 067705 (1999)
M. Andrews, M. Lewandowski, M. Trodden, D. Wesley, Phys. Rev. D 82, 105006 (2010)
D. Bazeia, J.D. Dantas, A.R. Gomes, L. Losano, R. Menezes, Phys. Rev. D 84, 045010 (2011)
C. Adam, J.M. Queiruga, Phys. Rev. D 84, 105028 (2011)
D. Bazeia, R. Menezes, Phys. Rev. D 84, 125018 (2011)
C. Adam, J.M. Queiruga, Phys. Rev. D 85, 025019 (2012)
D. Bazeia, J.D. Dantas, Phys. Rev. D 85, 067303 (2012)
D. Bazeia, E. da Hora, R. Menezes, H.P. de Oliveira, C. dos Santos, Phys. Rev. D 81, 125016 (2010)
D. Bazeia, A.S. Lobão Jr., R. Menezes, Phys. Rev. D 86, 125021 (2012)
Acknowledgements
The authors would like to thank C.A.G. Almeida, M. Pazetti and J.G.G.S. Ramos for comments and suggestions, and CAPES, CNPq and FAPESP for partial financial support. R. da Rocha thanks to CNPq grant 303027/2012-6.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bazeia, D., Losano, L., Menezes, R. et al. Study of models of the sine-Gordon type in flat and curved spacetime. Eur. Phys. J. C 73, 2499 (2013). https://doi.org/10.1140/epjc/s10052-013-2499-2
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjc/s10052-013-2499-2