Physics – Biological Physics
Scientific paper
1999-06-03
Physics
Biological Physics
19 pages, 6 figures, in Proc. "Nonlinear Cooperative Phenomena in Biological Systems", Ed.: L. Matsson (World Scientific, Sing
Scientific paper
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
Christiansen Peter L.
Gaididei Yuri B.
Johansson Magnus
Mingaleev Serge F.
Rasmussen Kim O.
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