标题： DNA分子非线性动力学中长程色散的影响 显示英文标题

标题： Effects of long-range dispersion in nonlinear dynamics of DNA molecules

摘要： 一个具有长程色散相互作用的离散非线性薛定谔（NLS）模型，用于描述DNA的动力学结构。 两种类型的色散相互作用：与距离的幂次依赖关系$r^{-s}$和指数依赖关系$e^{-\beta r}$，研究了$r$。 对于$s$小于某个临界值$s_{cr}$的情况，以及同样对于$\beta \leq \beta_{cr}$，在总能量的每个值处存在一个双稳态区间，其中存在两种稳定的静态状态：窄的、钉扎状态和宽的、移动状态。 对于三次非线性，孤子的双稳态发生在偶极-偶极色散相互作用 $(s=3)$时，以及在色散相互作用的倒数 $\beta \leq \beta_{cr}=1.67$时。 随着非线性程度的增加， $\sigma$，临界值 $s_{cr}$ 和 $\beta_{cr}$ 增加。 内在局域态的远距离行为取决于 $s$。 对于$s>3$，它们的尾部是指数型的，而对于$2<s<3$，它们的尾部是代数型的。 通过应用一种空间对称的扰动，形式为参数冲击，实现了固定态和移动态之间的受控转换。 该机制可能在控制DNA分子中的能量存储和传输中具有重要意义。 显示英文摘要

摘要： A discrete nonlinear Schrodinger (NLS) model with long-range dispersive interactions describing the dynamical structure of DNA is proposed. Dispersive interactions of two types: the power dependence $r^{-s}$ and the exponential dependence $e^{-\beta r}$ on the distance, $r$, are studied. For $s$ less than some critical value, $s_{cr}$, and similarly for $\beta \leq \beta_{cr}$ there is an interval of bistability where two stable stationary states: narrow, pinned states and broad, mobile states exist at each value of the total energy. For cubic nonlinearity the bistability of the solitons occurs for dipole-dipole dispersive interaction $(s=3)$, and for the inverse radius of the dispersive interaction $\beta \leq \beta_{cr}=1.67$. For increasing degree of nonlinearity, $\sigma$, the critical values $s_{cr}$ and $\beta_{cr}$ increase. The long-distance behavior of the intrinsically localized states depends on $s$. For $s>3$ their tails are exponential while for $2<s<3$ they are algebraic. A controlled switching between pinned and mobile states is demonstrated applying a spatially symmetric perturbation in the form of a parametric kick. The mechanism could be important for controlling energy storage and transport in DNA molecules.