Double Hierarchy and Dimensionalityof the Discommensuration Structuresin Terms of Hierarchical Matrix Rings

Abstract

It is shown that discrete sine-Gordon systems form a number of types of hierarchical discommensuration patterns simultaneously, with much different scales and different dimensions, which is the extension of one (type of) hierarchical discommensuration pattern with the system dimension which has already been shown. It is mathematically described by inverse matrix expansions and orthogonal transformations of the matrices which represent the structures of the system.