Abstract
A one-dimensional model is proposed, which ensures description of origination and main properties of longperiod and incommensurate phases of crystal having complex structure and consists of comparatively rigid “atomic clusters”. In the case where reciprocal rotations of theses clusters are considerably large, not only translational but also rotational degrees of freedom have to be taken into account for the clusters. It is consideration of the rotational degrees of freedom which might provide for formation of long-period states and development of a number of physical effects, such as a variety of soliton solutions (of domain walls) and their non-trivial dynamics.
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