A simple two-dimensional (2D) 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 (''20 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 (nontopological) soliton solutions which describe either (i) a supersonic solitary wave of longitudinal stretching accompanied by transverse slendering or, as in the 1D model, (ii) 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.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics, 1996, Vol 54, Issue 4, p. 3881-3894