The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model

doi:10.1088/1674-1056/17/9/039

中国物理B ›› 2008, Vol. 17 ›› Issue (9): 3378-3386.doi: 10.1088/1674-1056/17/9/039

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇下一篇

The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model

高秀云, 洪学仁, 王苍龙, 段文山

College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

收稿日期:2008-01-19 修回日期:2008-02-22 出版日期:2008-09-08 发布日期:2008-09-08
基金资助:
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

The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model

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)^†

College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China

Received:2008-01-19 Revised:2008-02-22 Online:2008-09-08 Published:2008-09-08
Supported by:
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

摘要/Abstract

摘要： 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.

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.

Key words: Sine--Gordon equation, Frenkel--Kontorova model, kink, breather

中图分类号: (Localized modes)

63.20.Pw

05.45.Yv (Solitons)

高秀云, 洪学仁, 王苍龙, 段文山. The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model[J]. 中国物理B, 2008, 17(9): 3378-3386.

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[J]. Chin. Phys. B, 2008, 17(9): 3378-3386.

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The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model

The dynamic characters of excitations in aone-dimensional Frenkel--Kontorova model

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