计及次近邻非谐相互作用下原子链中的非线性元激发

Nonlinear elementary excitations in a monoatomic chain with second nearest neighbour anharmonic interaction

利用多重尺度法 ,研究了谐振、非谐的近邻和次近邻相互作用下单原子链的晶格振动行为 ,发现非传播孤子在单原子链Brillouin区的任何位置均有可能存在 .与仅考虑最近邻相互作用下的单原子链的孤子群速相比 ,此时链中孤子的群速在Brillouin中央增大且衰减得更快 ;在Brillouin区会出现另一个群速为零的位置 .同时 。

By using a multiple scales method, we study the lattice vibration of a monoatomic chain taking into account the nearest neighbour and the second next nearest neighbour harmonic and anharmonic interactions. It is shown that nonpropagating solitons exist in any position of the Brillouin zone. Compared with that of a soliton in monoatomic chains with only nearest-neighbour interactions, the group velocity at the centre of the Brillouin zone is enhanced but attenuates more rapidly. In addition, a new position of zero velocity for the soliton is found in the first Brillouin. Our results show that the amplitude of this kind of soliton increases and the location of the soliton with the largest amplitude is close to the centre of the Brillouin zone.