Abstract A one-dimensional (1D) Frenkel--Kontorova (FK) model is studied numerically in this paper, and two new analytical solutions (a supersonic kink and a nonlinear periodic wave) of the Sine--Gordon (SG) equation (continuum limit approximation of the FK model) are obtained by using the Jacobi elliptic function expansion method. Taking these new solutions as initial conditions for the FK model, we numerically find there exist the supersonic kink and the nonlinear periodic wave in these systems and obtain a lot of interesting and significant results. Moreover, we also investigate the subsonic kink and the breather in these systems and obtain some new feature.
Received: 19 January 2008
Revised: 22 February 2008
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10575082), the Natural
Science Foundation of Gansu Province of China (Grant No
3ZS061-A25-013), the Natural Science Foundation of Northwest Normal
University of China (Grant N
Cite this article:
Gao Xiu-Yun(高秀云), Hong Xue-Ren(洪学仁), Wang Cang-Long(王苍龙), and Duan Wen-Shan(段文山) The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model 2008 Chin. Phys. B 17 3378
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