The main peculiarities which distinguish the models of polymer and nano-dimensional systems from conventional one- dimensional models are considered. They iunclude: appearance of coupled oscillations involving different types of motion; the formation of the solitons of a new type (e.g. of the extension instead the compression); existence of optic breathers even in one- component chains; «quantization» of the soliton-like excitations as a consequence of geometric restrictions. On this basis the mechanisms of significant physical processes, which can not proceed without localized nonlinear excitations, have been analyzed. Among them are: the structural transformations in polymer crystals (in particular, the transitions between monoclinic and orthorhombic phases); dielectric and mechanical relaxation in the slightly oxidized polyethylene; anomalous electro- conductivity in the polymers with the conjugate bonds; «superfast» propagation of exothermal chemical reactions in molecular crystals.
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