Nonlinear dynamics of zigzag molecular chains

Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the nonlinear dynamics of a chain changes dramatically on switching from the one-dimensional linear chain to the more realistic planar zigzag model - due, in particular, to geometry-dependent anharmonicity that comes into the picture. The existence or otherwise of solitons is determined by the interplay between the geometrical anharmonicity and the physical anharmonicity of the intersite interaction, one of opposite sign from the other. The nonlinear dynamical analysis of three most typical zigzag models (two-dimensional alpha helix, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure limits the soliton dynamics to finite, relatively narrow, supersonic solitons velocity intervals and may also result in that different soliton types (such as tension and compression varieties) develop simultaneously in the chain. Accordingly, the inclusion of chain geometry is necessary if physical phenomena are to be described in terms of solitary waves.