Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2005-09-27
Nonlinear Sciences
Pattern Formation and Solitons
Published version. 21 pages, 5 figures. Section 3 completely re-written. Conclusions unchanged
Scientific paper
10.1088/0951-7715/19/6/008
It is shown that the topological discrete sine-Gordon system introduced by Speight and Ward models the dynamics of an infinite uniform chain of electric dipoles constrained to rotate in a plane containing the chain. Such a chain admits a novel type of static kink solution which may occupy any position relative to the spatial lattice and experiences no Peierls-Nabarro barrier. Consequently the dynamics of a single kink is highly continuum like, despite the strongly discrete nature of the model. Static multikinks and kink-antikink pairs are constructed, and it is shown that all such static solutions are unstable. Exact propagating kinks are sought numerically using the pseudo-spectral method, but it is found that none exist, except, perhaps, at very low speed.
Speight Martin J.
Zolotaryuk Yaroslav
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