Different kinds of discrete breathers in a Sine–Gordon lattice

Abstract

We study a one-dimensional Sine–Gordon lattice of anharmonic oscillators with cubic and quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the one-dimensional Sine–Gordon lattice no matter whether the nonlinear interaction is cubic or quartic. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.

Keywords

discrete breathers / quasiperiodic discrete breathers / chaotic discrete breathers / Sine–Gordon lattice

References

[1] S. Aubry, Physica D, 1997, 103: 201

[2] S. Flach, C. R. Willis, Phys. Rep., 1998, 295: 181

[3] S. Aubry, Physica D, 2006, 216: 1

[4] S. Flach, Computational Studies of Discrete Breathers, in: Energy Localization and Transfer, edited by T. Dauxois, A. Litvak-Hinenzon, R. MacKay, and A. Spanoudaki, Singapore: World Scientific, 2004: 1-71

[5] S. Flach and A. Gorbach, Phys. Rep., 2008, 467: 1

[6] Q. Zhou, B. B. LÜ, and Q. Tian, Acta. Phys. Sin., 2009, 58(1): 0411 (in Chinese)

[7] B. B. LÜ and Q. Tian, Front. Phys. China, 2009, 4(4): 497

[8] B. B. LÜ, Q. Zhou, and Q. Tian, Journal of Beijing Normal University (Natural Science), 2008, 44(5): 476 (in Chinese)

[9] B. B. LÜ and Q. Tian, Journal of Beijing Normal University (Natural Science), 2008, 44(6): 581 (in Chinese)

[10] B. B. LÜ and Q. Tian, Chin. Phys., 2009, 18 (in press)

[11] B. B. LÜ and Q. Tian, Chin. Phys., 2009 (in press)

[12] M. Johansson and S. Aubry, Nonlinearity, 1997, 10:11571

[13] P. G. Kevrekidis and M. I. Weinstein, Mathematics and Computers in Simulation, 2003, 62: 65

[14] G. M. Chechin, G. S. Dzhelauhova, and E. A. Mehonoshina, Phys. Rev. E, 2006, 74: 036608

[15] V. M. Burlakov, S. A. Kiselev, and V. I. Rupasov, Phys. Lett. A, 1990, 147: 130

[16] K. Ikeda, Y. Doi, F. F. Bao, and T. Kawahara, Physica D, 2007, 225(2): 184

[17] P. J. Martinez, M. Meister, L. M. Floria, and F. Falo, Chaos, 2003, 13: 610

[18] P. Mainadis and T. Bountis, Phys. Rev. E, 2006, 73: 046211

[19] Y. C. Kouomou, P. Colet, L. Larger, and N. Gastaud, Phys. Rev. Lett., 2005, 95: 203903

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg