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

A discrete nonlinear Schrödinger (NLS) model with long-range dispersive interactions describing the dynamical structure of DNA is proposed. Dispersive interactions of two types: the power dependence r and the exponential dependence e r on the distance, r, are studied. For s less than some critical value, scr, and similarly for β ≤ βcr 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 β ≤ βcr = 1.67. For increasing degree of nonlinearity, σ, the critical values scr and βcr 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.