Two-dimensional dynamics of a free molecular chain with a secondary structure

A simple two-dimensional ͑2D͒ model of an isolated (free) molecular chain with primary and secondary structures has been suggested and investigated both analytically and numerically. This model can be considered as the simplest generalization of the well-known Fermi-Pasta-Ulam model of an anharmonic chain in order to include transverse degrees of freedom of the chain molecules. Both the structures are provided by the first-and second-neighbor intermolecular bonds, respectively, resulting in a regular zig-zag (''2D helix'') chain on a plane. The set of two coupled nonlinear field equations with respect to the longitudinal and transverse displacements of the chain molecules has been derived. Two types of stable ͑nontopological͒ soliton solutions which describe either ͑i͒ a supersonic solitary wave of longitudinal stretching accompanied by transverse slendering or, as in the 1D model, ͑ii͒ supersonic pulses of longitudinal compression propagating together with localized transverse thickening (bulge) have been found. Some peculiar stability properties of these two-component soliton solutions have been discovered by using numerical techniques developed in this paper. ͓S1063-651X͑96͒10809-6

Interplay of nonlinearity and geometry in a DNA-related, Klein-Gordon model with long-range dipole-dipole interaction

Most of the studies on mathematical models of DNA are limited to next neighbor interaction. However, the coupling between base pairs is thought to be caused by dipole interaction, and, when the DNA strand is bent, the distances between base pairs become shorter, therefore the interactions with distant base pairs have to be taken into account. In this paper we analyze the existence and stability of breathers, i.e., localized oscillations in a simple model of bent DNA with long-range dipole interaction. Breathers have been suggested as precursors of the denaturation bubble