Non-symmetric kinks in Klein-Gordon chains free of the Peierls-Nabarro potential

[摘要] There exist several approaches to discretize Klein-Gordon field equations in a way that static kink solutions can be obtained from a two-point map, iteratively, starting from any admissible initial value. Such kinks can be placed anywhere with respect to the lattice, in other words, they do not experience the Peierls-Nabarro potential (PNP). So far, to the best of our knowledge, only symmetric PNP-free kinks have been analyzed for the φ 4 and sine-Gordon equations. It is interesting to construct PNP-free discretisations for the φ 6 equation supporting asymmetric kinks. In the present study, two versions of such discretisations are derived.

[发布机构] Institute for Metals Superplasticity Problems, Ufa; 450001, Russia^1;Department of Mathematics and Statistics, University of Massachusetts, Amherst; MA; 01003, United States^2;National Research Tomsk State University, Tomsk; 634050, Russia^3

[关键词] Kink solution;Klein-Gordon chain;Klein-Gordon fields;Peierls-Nabarro potential;Two-point