Nonlinear dynamics of zigzag molecular chains

Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the non-linear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model — due, in particular, to the geometry-dependent anharmonism that comes into the picture. The existence or otherwise of solitons is determined in this case by the interplay between the geometrical anharmonism and the physical anharmonism of the interstitial interaction, of opposite signs. The nonlinear dynamic analysis of the three most typical zigzag models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton types (such as extension 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.