中国物理B ›› 2008, Vol. 17 ›› Issue (4): 1331-1340.doi: 10.1088/1674-1056/17/4/030

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Existences and stabilities of bright and dark breathers in a general one-dimensional discrete monatomic Chain

田强1, 汤凤云2, 徐权3   

  1. (1)Department of Physics, Beijing Normal University, Beijing 100875, China; (2)Department of Physics, Beijing Normal University, Beijing 100875, China;Daqing 3th middle school, Daqing 163712, China; (3)Scientific and Technological Office, Daqing Normal University, Daqing 163712, China;Department of Physics, Beijing Normal University, Beijing 100875, China
  • 收稿日期:2007-04-25 修回日期:2007-10-29 出版日期:2008-04-20 发布日期:2008-04-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10574011) and Natural Science Foundation of Heilongjiang Province, China (Grant No A200506).

Existences and stabilities of bright and dark breathers in a general one-dimensional discrete monatomic Chain

Xu Quan(徐权)a)b), Tang Feng-Yun(汤凤云)b)c), and Tian Qiang(田强)b)†   

  1. a Scientific and Technological Office, Daqing Normal University, Daqing 163712, China; b Department of Physics, Beijing Normal University, Beijing 100875, China; c Daqing 3th middle school, Daqing 163712, China
  • Received:2007-04-25 Revised:2007-10-29 Online:2008-04-20 Published:2008-04-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10574011) and Natural Science Foundation of Heilongjiang Province, China (Grant No A200506).

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摘要： A general one-dimensional discrete monatomic model is investigated by using the multiple-method. It is proven that the discrete bright breathers (DBBs) and discrete dark breathers (DDBs) exist in this model at the anti-continuous limit, and then the concrete models of the DBBs and DDBs are also presented by the multiple-scale approach (MSA) and the quasi-discreteness approach (QDA). When the results are applied to some particular models, the same conclusions as those presented in corresponding references are achieved. In addition, we use the method of the linearization analysis to investigate this system without the high order terms of $\varepsilon$. It is found that the DBBs and DDBs are linearly stable only when coupling parameter $\chi$ is small, of which the limited value is obtained by using an analytical method.

关键词: discrete bright breather, discrete dark breather, linear stability, anti-continuous limit

Abstract: A general one-dimensional discrete monatomic model is investigated by using the multiple-method. It is proven that the discrete bright breathers (DBBs) and discrete dark breathers (DDBs) exist in this model at the anti-continuous limit, and then the concrete models of the DBBs and DDBs are also presented by the multiple-scale approach (MSA) and the quasi-discreteness approach (QDA). When the results are applied to some particular models, the same conclusions as those presented in corresponding references are achieved. In addition, we use the method of the linearization analysis to investigate this system without the high order terms of $\varepsilon$. It is found that the DBBs and DDBs are linearly stable only when coupling parameter $\chi$ is small, of which the limited value is obtained by using an analytical method.

Key words: discrete bright breather, discrete dark breather, linear stability, anti-continuous limit

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
63.20.Pw (Localized modes)