Abstract
By means of systematic simulations, we study the motion of discrete solitons in weakly dissipative Toda lattices (TLs) with periodic boundary conditions, resonantly driven by a spatially staggered time-periodic (ac) force. A complex set of alternating stability bands and instability gaps, including scattered isolated stability points, is revealed in the parametric plane of the soliton’s velocity and forcing amplitude for a given size of the circular lattice. The analysis is also reported for the circular TL including a single light- or heavymass defect. The stability chart as a whole shrinks and eventually disappears with the increase of the lattice’s size and strength of the mass defect. Qualitative explanations to these findings are proposed. We also report the dependence of the stability area on the initial position of the soliton, finding that the area is largest for some intersite position. For a pair of solitons traveling in opposite directions, there exist regimes where both solitons survive periodic collisions in small-size lattices.
[1] M. Sato, B. E. Hubbard, A. J. Sievers, Rev. Mod. Phys. 78, 137 (2006) http://dx.doi.org/10.1103/RevModPhys.78.13710.1103/RevModPhys.78.137Search in Google Scholar
[2] F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, Phys. Rep. 463, 1 (2008) http://dx.doi.org/10.1016/j.physrep.2008.04.00410.1016/j.physrep.2008.04.004Search in Google Scholar
[3] Y. V. Kartashov, B. A. Malomed, L. Torner, Rev. Mod. Phys. 83, 247 (2011) http://dx.doi.org/10.1103/RevModPhys.83.24710.1103/RevModPhys.83.247Search in Google Scholar
[4] T. Dauxois, R. MacKay, G. Tsironis (Ed.), Nonlinear Physics: Condensed Matter, Dynamical, Systems and Biophysics — A Special Issue dedicated to Serge Aubry, Physica D 216,Issue 1, 1–246 (2006) Search in Google Scholar
[5] M. Toda, J. Phys. Soc. Jpn. 23, 501 (1967) http://dx.doi.org/10.1143/JPSJ.23.50110.1143/JPSJ.23.501Search in Google Scholar
[6] M. Toda, Phys. Rep. 18, 1 (1973) http://dx.doi.org/10.1016/0370-1573(75)90018-610.1016/0370-1573(75)90018-6Search in Google Scholar
[7] T. Kuusela, J. Hietarinta, Physica D 41, 322 (1990) http://dx.doi.org/10.1016/0167-2789(90)90002-710.1016/0167-2789(90)90002-7Search in Google Scholar
[8] G. Friesecke, J. A. D. Wattis, Comm. Math. Phys. 161, 391 (1994) http://dx.doi.org/10.1007/BF0209978410.1007/BF02099784Search in Google Scholar
[9] N. J. Zabusky, Z. Sun, G. Peng, Chaos 16, 013130 (2006) http://dx.doi.org/10.1063/1.216559210.1063/1.2165592Search in Google Scholar PubMed
[10] T. Jin, H. Zhao, B. B. Hu, Phys. Rev. E 81, 037601 (2010) http://dx.doi.org/10.1103/PhysRevE.81.03760110.1103/PhysRevE.81.037601Search in Google Scholar PubMed
[11] A. Nakamura, S. Takeno, Progr. Theor. Phys. 58, 1074 (1977) http://dx.doi.org/10.1143/PTP.58.107410.1143/PTP.58.1074Search in Google Scholar
[12] A. Nakamura, Progr. Theor. Phys. 59, 1447 (1978) http://dx.doi.org/10.1143/PTP.59.144710.1143/PTP.59.1447Search in Google Scholar
[13] F. Yoshida, T. Sakuma, Progr. Theor. Phys. 67, 1379 (1982) http://dx.doi.org/10.1143/PTP.67.137910.1143/PTP.67.1379Search in Google Scholar
[14] T. Iizuka, M. Wadati, J. Phys. Soc. Jpn. 62, 1932 (1993) http://dx.doi.org/10.1143/JPSJ.62.193210.1143/JPSJ.62.1932Search in Google Scholar
[15] G. Matsui, J. Phys. Soc. Jpn. 65, 2447 (1996) http://dx.doi.org/10.1143/JPSJ.65.244710.1143/JPSJ.65.2447Search in Google Scholar
[16] M. Leo, R. A. Leo, A. Scarsella, G. Soliani, Eur. Phys. J. D 11, 327 (2000) http://dx.doi.org/10.1007/s10053007005910.1007/s100530070059Search in Google Scholar
[17] L. Vergara, B. A. Malomed, Phys. Rev. E 77, 047601 (2008) http://dx.doi.org/10.1103/PhysRevE.77.04760110.1103/PhysRevE.77.047601Search in Google Scholar PubMed
[18] A. Nakamura, Progr. Theor. Phys. 61, 427 (1979) http://dx.doi.org/10.1143/PTP.61.42710.1143/PTP.61.427Search in Google Scholar
[19] A. Nakamura, S. Takeno, Progr. Theor. Phys. 62, 33 (1979) http://dx.doi.org/10.1143/PTP.62.3310.1143/PTP.62.33Search in Google Scholar
[20] Y. Kubota, T. Odagaki, Phys. Rev. E 71, 016605 (2005) http://dx.doi.org/10.1103/PhysRevE.71.01660510.1103/PhysRevE.71.016605Search in Google Scholar PubMed
[21] Y. Kubota, T. Odagaki, J. Phys. A: Math. Gen. 39, 12343 (2006) http://dx.doi.org/10.1088/0305-4470/39/40/00410.1088/0305-4470/39/40/004Search in Google Scholar
[22] L. Vergara, Phys. Rev. Lett. 95, 108002 (2005) http://dx.doi.org/10.1103/PhysRevLett.95.10800210.1103/PhysRevLett.95.108002Search in Google Scholar
[23] L. L. Bonilla, B. A. Malomed, Phys. Rev. B 43, 11539 (1991) http://dx.doi.org/10.1103/PhysRevB.43.1153910.1103/PhysRevB.43.11539Search in Google Scholar
[24] B. A. Malomed, Phys. Rev. A 45, 4097 (1992) http://dx.doi.org/10.1103/PhysRevA.45.409710.1103/PhysRevA.45.4097Search in Google Scholar
[25] T. Kuusela, J. Hietarinta, B.A. Malomed, J. Phys. A: Math. Gen. 26, L21 (1993) http://dx.doi.org/10.1088/0305-4470/26/1/00510.1088/0305-4470/26/1/005Search in Google Scholar
[26] K. O. Rasmussen, B. A. Malomed, A. R. Bishop, N. Gronbech-Jensen, Phys. Rev. E 58, 6695 (1998) http://dx.doi.org/10.1103/PhysRevE.58.669510.1103/PhysRevE.58.6695Search in Google Scholar
[27] T. Kuusela, Phys. Lett. A 167, 54 (1992) http://dx.doi.org/10.1016/0375-9601(92)90625-V10.1016/0375-9601(92)90625-VSearch in Google Scholar
[28] T. Kuusela, Chaos Sol. Fract. 5, 2419 (1995) http://dx.doi.org/10.1016/0960-0779(94)E0107-Z10.1016/0960-0779(94)E0107-ZSearch in Google Scholar
[29] J. Hietarinta, T. Kuusela, B. A. Malomed, J. Phys. A: Math. Gen. 28, 3015 (1995) http://dx.doi.org/10.1088/0305-4470/28/11/00710.1088/0305-4470/28/11/007Search in Google Scholar
[30] E. Hairer, S. P. Norset, G. Wanner, Solving Ordinary Differential Equations: I. Nonstiff Problems, 2nd Edition, Springer Series in Computational Mathematics vol. 8 (Springer-Verlag, Berilin-Heidelberg, 1993) Search in Google Scholar
[31] H. -C. Chang, E. A. Demekhin, D. I. Kopelevich, Phys. Rev. Lett. 75, 1747 (1995) http://dx.doi.org/10.1103/PhysRevLett.75.174710.1103/PhysRevLett.75.1747Search in Google Scholar PubMed
[32] B. A. Malomed, B. -F. Feng, T. Kawahara, Phys. Rev. E 64, 046304 (2001) http://dx.doi.org/10.1103/PhysRevE.64.04630410.1103/PhysRevE.64.046304Search in Google Scholar PubMed
[33] E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993) Search in Google Scholar
[34] E. Hairer, G. Wanner, Solving Ordinary Differential Equations: II. Stiff and Differential-Algebraic Problems (Springer-Verlag, Berlin-Heidelberg, 1991) http://dx.doi.org/10.1007/978-3-662-09947-610.1007/978-3-662-09947-6Search in Google Scholar
© 2013 Versita Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
