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 kx = ky = kz = k and k = ±π/6α0 in the Brillouin zone, as well as has 3D vortices in the direction of kx = ky = kz = k and k = ±π/α0 in the Brillouin zone.
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 kx = ky = kz = k and k = ±π/6α0 in the Brillouin zone, as well as has 3D vortices in the direction of kx = ky = kz = k and k = ±π/α0 in the Brillouin zone.
基金
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）.
