阻尼作用下一维非线性单原子链中的孤子

SOLITONS IN ONE-DIMENSIONAL NONLINEAR MONOATOMIC CHAIN UNDER DAMPING

利用多重尺度法 ,研究了弱阻尼作用下一维非线性单原子链中的波动行为 ,发现在O(ε)级阻尼作用下其格波幅度减小 ,群速变慢 .在晶格动力学中导出了参数耗散型非线性Schr dinger方程 ,对方程进行解析求解 .结果表明 :在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子 ;在O(ε2 )级阻尼作用下 ,格孤波为钟状或扭结的孤子 .

By virtue of the method of multiple scales, we have investigated the behavior of waves in a one-dimensional nonlinear monoatomic chain under damping and found that the amplitude of the lattice waves decreases and the group velocity becomes slow under the action of damping of an order of O(ε). At the same time, we have derived PDNLS equation and obtained its analytical solution. Our results show that: there exists propagating envelope soliton in the one-dimensional nonlinear monoatomic chain under the damping, provided the damping is of an order of O(ε). However, the chain supports the propagation of the soliton of bell shape or kink as the damping is of an order of O(ε2).