中国物理B ›› 2006, Vol. 15 ›› Issue (2): 253-265.doi: 10.1088/1009-1963/15/2/003

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The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity

田强1, 徐权2   

  1. (1)Department of Physics, Beijing Normal University, Beijing 100875, China; (2)Scientific and Technological Office, Daqing Normal University, Daqing 163712, China
  • 收稿日期:2005-05-27 修回日期:2005-07-25 出版日期:2006-02-20 发布日期:2006-02-20
  • 基金资助:
    Project supported by the Foundation for University Key Teachers by the Ministry of Education of China, the Scientific Research Fund of Heilongjiang Provincial Education Department (Grant No 10543080) and Natural Science Foundation of Heilongjiang Province, China (Grant No A200506).

The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity

Xu Quan (徐权)a, 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
  • Received:2005-05-27 Revised:2005-07-25 Online:2006-02-20 Published:2006-02-20
  • Supported by:
    Project supported by the Foundation for University Key Teachers by the Ministry of Education of China, the Scientific Research Fund of Heilongjiang Provincial Education Department (Grant No 10543080) and Natural Science Foundation of Heilongjiang Province, China (Grant No A200506).

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摘要： By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a 1D discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/6$a_{0}$ in the Brillouin zone, as well as has 3D vortices in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/$a_{0}$ in the Brillouin zone.

关键词: 3D simple cubic lattice, Brillouin zone, envelop soliton, distorted soliton, vortices

Abstract: By virtue of the method of multiple-scale and the quasi-discreteness approach, we have discussed the nonlinear vibration equation of a 3D discrete monatomic lattice with its nearest-neighbours interaction. The 3D simple cubic lattices have the same localized modes as a 1D discrete monatomic chain with cubic and quartic nonlinearity. The nonlinear vibration in the 3D simple cubic lattice has 3D distorted solitons and 3D envelop solitons in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/6$a_{0}$ in the Brillouin zone, as well as has 3D vortices in the direction of $k_{x}=k_{y}=k_{z}=k$ and $k=\pm \pi$/$a_{0}$ in the Brillouin zone.

Key words: 3D simple cubic lattice, Brillouin zone, envelop soliton, distorted soliton, vortices

中图分类号:  (Theory of crystal structure, crystal symmetry; calculations and modeling)

  • 61.50.Ah
63.20.K- (Phonon interactions) 05.45.Yv (Solitons)