Discrete Klein-Gordon models with static kinks free of the Peierls-Nabarro potential

Abstract

For the nonlinear Klein-Gordon type models, we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice. These discrete models are therefore free of the {\it static} Peierls-Nabarro potential. Previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method. A relevant physical consequence of our findings is the existence of a wide class of discrete Klein-Gordon models where slow kinks {\it practically} do not experience the action of the Peierls-Nabarro potential. Such kinks are not trapped by the lattice and they can be accelerated by even weak external fields.

6 pages, 2 figures

References in corpus (9)

• Kink dynamics in a novel discrete sine-Gordon system
• Translationally invariant discrete kinks from one-dimensional maps
• Topological discrete kinks
• Moving lattice kinks and pulses: an inverse method
• Dynamics of Lattice Kinks
• A discrete phi^4 system without Peierls-Nabarro barrier
• Universal Scaling of Wave Propagation Failure in Arrays of Coupled Nonlinear Cells
• Standard Nearest Neighbor Discretizations of Klein-Gordon Models Cannot Preserve Both Energy and Linear Momentum
• Discrete kink dynamics in hydrogen-bonded chains I: The one-component model

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