【摘要】 运用连续极限近似的方法,求解二维单原子晶格的非线性振动方程,当晶格为二维各向同性时,可以得出在只考虑最近邻相互作用和分别考虑3次非线性效应、4次非线性效应以及3次、4次非线性效应同时存在的条件下,二维单原子晶格的非线性振动行为分别由KdV、MKdV和GKdV方程描述,具有扭结孤子解;通过讨论还得出使二维各向同性晶格非线性行为减小或消失的途径,即3次非线性的正效应和4次非线性效应的相互作用结果就可以减小晶格的非线性行为,当3次非线性的正效应因子σ=+1000时,二维各向同性晶格非线性行为将彻底消失.更多还原

【Abstract】 The equations of nonlinear vibration in two-dimensional monoatomic lattice were solved by virtue of the method of continuum limit. When the lattice is the two-dimensional monoatomic lattice with identical qualities in every directions and the nearest-neighbor interaction is taken into account, the authors obtaine that the nonlinear vibration in the two-dimensional monoatomic lattice with cubic nonlinearity, quartic nonlinearity and cubic and quartic nonlinearity are described respectively by the KdV, MKdV and GKdV equations, and have the kink-solitons. This paper gains that the nonlinearity is weakened and distinguished by the interaction of positive cubic nonlinearity with quartic nonlinearity. When the cubic nonlinear factor σ=+1()000, the nonlinear behaviors of two-dimensional monoatomic lattice with identical qualities in every directions disappear completely.更多还原