Kinks in dipole chains

Abstract

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.

Published version. 21 pages, 5 figures. Section 3 completely re-written. Conclusions unchanged

References in corpus (4)

• Translationally invariant discrete kinks from one-dimensional maps
• Travelling kinks in discrete phi^4 models
• Discrete Klein-Gordon models with static kinks free of the Peierls-Nabarro potential
• Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum

Cited by in corpus (11)

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• Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum
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• Discrete Nonlinear Schrodinger Equations with arbitrarily high order nonlinearities
• Comparative Study of Different Discretizations of the ${\varphi }^4$ Model
• High-speed kinks in a generalized discrete ${\varphi }^4$ model
• Exact static solutions to a translationally invariant discrete ${\varphi }^4$ model
• Collision of ${\varphi }^4$ kinks free of the Peierls-Nabarro barrier in the regime of strong discreteness
• On a Class of Spatial Discretizations of Equations of the Nonlinear Schrodinger Type
• Nanopteron solution of the Korteweg-de Vries equation
• On the kinks in discrete systems