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
a Scientific and Technological Office, Daqing Normal University, Daqing 163712, China; b Department of Physics, Beijing Normal University, Beijing 100875, China
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.
Received: 27 May 2005
Revised: 25 July 2005
Accepted manuscript online:
PACS:
61.50.Ah
(Theory of crystal structure, crystal symmetry; calculations and modeling)
Fund: 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).
Cite this article:
Xu Quan (徐权), Tian Qiang (田强) The 3D solitons and vortices in 3D discrete monatomic lattices with cubic and quartic nonlinearity 2006 Chinese Physics 15 253
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