中文摘要：

研究了一维更键海森伯反铁磁链的孤子激发问题。在该反铁磁链模型的哈密顿量中,考虑了格点间的最近邻及次近邻相互作用、Dzyaloshinskii-Moriya相互作用和恒定外磁场的影响。利用Holstain-Primakoff变换、多重尺度方法,得到了系统不考虑非线性项时自旋波的频率ω和考虑非线性项时两套格子所对应的两个亮孤子解。在此基础上,讨论了波数k、更键强度m（即最近邻交换作用比值J＇1/J1）对ω和孤子峰值、宽度、能量的影响。研究表明：ω可以分为光学支ω＋和声学支ω-,在kb=0,±2π附近（b为最近邻元胞间距）,ω并不存在;声学支ω-有对应的亮孤子解,光学支则没有;J1一定时,m越小,ω两分支间间隙越小;参数相同时,两个亮孤子解的孤子峰宽、相速、群速、能量量子相同,包络振幅和相位不同;两孤子解能量量子小于不考虑非线性项时的自旋波能量量子,两孤子解是稳定解;m的大小不仅影响两孤子的相对峰值大小,还影响两孤子的相对相位。两孤子解的峰值大小随m、k的变化而变,但变化并不一致。两孤子的峰宽既没有随k单调增减,也没有随m单调增减。

英文摘要：

The soliton excitation of a one-dimensional Heisenberg antiferromagnetic chain with bond alternation was studied. In the Hamiltonian of this antiferromagnetic model,the interactions between the nearest neighbor lattice and next nearest neighbor lattice,Dzyaloshinskii-Moriya interaction and constant external magnetic field were considered. By using Holstain-Primakoff transformation and the multi-scale method,spin wave frequency ω was obtained when nonlinear term in the system was neglect,and two bright soliton solutions of the two sets of sublattice were obtained when nonlinear term was considered. Finally,the effects of the wave vector k and bond alternation strength m（ the nearest exchange interaction parameter ratios J＇1/ J1） on ω,the soliton peak value,width and energy were discussed. The results show that ω can be divided into optical branch ω＋and acoustic branch ω-. ω does not exist near kb = 0,± 2π（ b is the distance between the two nearest neighbor cells）. Acoustic branch ω-corresponds to bright soliton solution,optical does not. When J1 is certain,the smaller the m is,the smaller the gap between ω＋and ω-will be. The peak width,phase velocity,group velocity and energy quantum of the two bright soliton solutions are of the same values,but the envelop amplitude and phase are different with thesame parameter. The energy quantum of the soliton solutions is smaller than the energy quantum of the spin wave solution when nonlinear term is not considered,so the two soliton solution is stable. The m affects not only the relative peak value,but also the relative phase of the two solitons. The peak value of two soliton solutions vary with the changes of m and k,but the change is not the same. The peak width does not increase monotonously with the crease of k,nor does it increase monotonously with that of m.