Propagation of solitons in the Toda lattice with an impure segment
Propagation of solitons in the Toda lattice with an impure segment
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具有不纯段的户田晶格中孤子的传播
DOI：
10.1103/physreve.61.3133
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
T. Odagaki
中科院分区：
文献类型：
--
作者：
Y. Kubota;T. Odagaki
数值研究了单孤子在含有两种质量的不纯段的户田晶格中的传输和散射。入射孤子被不纯段分裂为透射孤子、反射孤子和俘获孤子。被捕获在段中的孤子的能量从段中逃逸非常缓慢，因此我们可以通过透射孤子和入射孤子的能量之比来定义透射率。结果表明，传输速率对段长度N的依赖关系可以很好地拟合为1/（1+\ensuremath{\alpha}{N}^{\ensuremath{\beta}}）。传输率也是入射孤子波数的单调递减函数。透射波的大部分能量由前沿的大孤子（前沿孤子）携带，这是户田晶格的精确孤子。当质量差很小时，可以通过将段视为单元的重复并重复由于单元引起的波数的重整化来获得透射率。
The transmission and scattering of a single soliton is studied numerically in the Toda lattice with an impure segment which consists of two kinds of masses. The incident soliton is split into transmitted, reflected, and trapped solitons by the impure segment. The energy of the soliton trapped in the segment escapes from the segment very slowly and thus we can define the transmission rate by the ratio of energies of the transmitted soliton and the incident soliton. It is shown that the dependence of the transmission rate on the segment length N can be fitted quite well by $1/(1+\ensuremath{\alpha}{N}^{\ensuremath{\beta}}).$ The transmission rate is also shown to be a monotone decreasing function of the wave number of the incident soliton. Most of the energy of the transmitted wave is carried by a large soliton (the frontier soliton) at the front, which is shown to be an exact soliton of the Toda lattice. When the mass difference is small, the transmission rate can be obtained by considering the segment as a repetition of a unit and repeating the renormalization of the wave number due to the unit.