Abstract.
It is shown, concerning equivalent classes, that on a one-dimensional lattice with nearest neighbour interaction, there are only four independent models possessing double-shocks. Evolution of the width of the double-shocks in different models is investigated. Double-shocks may vanish, and the final state is a state with no shock. There is a model for which at large times the average width of double-shocks will become smaller. Although there may exist stationary single-shocks in nearest neighbour reaction diffusion models, it is seen that in none of these models, there exist any stationary double-shocks. Models admitting multi-shocks are classified, and the long period behaviour of multi-shock solutions is also investigated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Derrida, L. Lebowitz, E. R. Speer, J. Stat. Phys. 89, 135 (1997)
V. Popkov, G.M. Schütz, J. Stat. Phys. 112, 523 (2003)
V. Belitsky, G.M. Schütz, Electron. J. Prob. 7, 1 (2002)
K. Krebs, F.H. Jafarpour, G.M. Schütz, New J. Phys. 5, 145.1 (2003)
C. Pigorsch, G.M. Schütz, J. Phys. A 33, 7919 (2000)
F.H. Jafarpour, Phys. Lett. A 326, 14 (2004)
M. Paessens, G.M. Schütz, New J. Phys. 6, 120 (2004)
F.H. Jafarpour, F.E. Ghafari, S.R. Masharian, J. Phys. A 38, 4579 (2005)
F.H. Jafarpour, Physica A 358, 413 (2005)
F.H. Jafarpour, S.R. Masharian, Phys. Rev. E 70, 056121 (2004)
A. Rákos, G.M. Schütz, J. Stat. Phys. 117, 55 (2004)
V. Popkov, A. Rakos, R.D. Willmann, A.B. Kolomeisky, G.M. Schütz, Phys. Rev. E 67, 066117 (2003)
S. Mukherji, S.M. Bhattacharjee, J. Phys. A 38, L285 (2005)
A. Parmeggiani, T. Franosch, E. Fraey, Phys. Rev. Lett. 90, 086601 (2003)
A. Rakos, M. Paessens, G.M. Schütz, Phys. Rev. Lett. 91, 238302 (2003)
M.R. Evans, R. Juhasz, L. Santen, Phys. Rev. E 68, 026117 (2003)
S.M. Bhattacharjee, e-print arXiv:cond-mat/0604444
M. Arabsalmani, A. Aghamohammadi, Phys. Rev. E 74, 011107 (2006)
M. Khorrami, A. Aghamohammadi, Phys. Rev. E 63, 042102 (2001)
N. Majd, A. Aghamohammadi, M. Khorrami, Phys. Rev. E 64, 046105 (2001)
M. Khorrami, A. Aghamohammadi, Phys. Rev. E 65, 056129 (2002)
A. Aghamohammadi, M. Khorrami, J. Phys. A 34, 7431 (2001)
A. Aghamohammadi, M. Khorrami, J. Phys. A 33, 7843 (2000)
F. Roshani, A. Aghamohammadi, M. Khorrami, Phys. Rev. E 70, 056128 (2004)
F.C. Alcaraz, M. Droz, M. Henkel, V. Rittenberg, Ann. Phys. 230, 250 (1994)
K. Krebs, M.P. Pfannmuller, B. Wehefritz, H. Hinrichsen, J. Stat. Phys. 78 [FS], 1429 (1995)
G.M. Schütz, E. Domany, J. Stat. Phys. 72, 277 (1993); S. Sandow; Phys. Rev. E 50, 2660 (1994); K. Mallick, S. Sandow, J. Phys. A 30, 4513 (1997)
G. Schütz, J. Stat. Phys. 79, 243 (1995)
A. Aghamohammadi, A.H. Fatollahi, M. Khorrami, A. Shariati, Phys. Rev. E 62, 4642 (2000)
A. Shariati, A. Aghamohammadi, M. Khorrami, Phys. Rev. E 64, 066102 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Arabsalmani, M., Aghamohammadi, A. Multi-shocks in reaction-diffusion models. Eur. Phys. J. B 55, 439–446 (2007). https://doi.org/10.1140/epjb/e2007-00069-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2007-00069-7