离散非均匀非线性Schrodinger方程的数值研究

本文用数值方法研究了商教非线性非均匀Schrodinger方程,讨论了孤子被势垒,势阱散射的性质,计算结果表明,在非均匀的一维分子链上的长距离输运也是可能的。

A Numerical Research of the Discrete Heterogeneous Nonlinear Schrodinger Equations

In the continous approximation, the discrete nonlinear equations are re- duced to the common nonlinear equation, and the soliton solution is obtained. However, the continuous approximation may not be used and there must be some heterogeneities in natural biological systems of large molecules. Under little weakened condi- tions, it is proved that there are approximate solition solutions and the soliton velocities has an upper limit. The scattering of the soliton by some potential barriers and wells are re- searched by numerical methods. All the calculations come to the conclusion that there can be long-distance transportations even in some heterogencous one-dimensional molecular chains.