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arXiv · 2012.15594

On the existence of solutions for Frenkel-Kontorova models on quasi-crystals

Jianxing Du·Xifeng Su
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Abstract

This article focuses on recent investigations on equilibria of the Frenkel-Kontorova models subjected to potentials generated by quasi-crystals. We present a specific one-dimensional model with an explicit potential driven by the Fibonacci quasi-crystal. For a given positive number $\theta$, we show that there are multiple equilibria with rotation number $\theta$, e.g., a minimal configuration and a non-minimal equilibrium configuration. Some numerical experiments verifying the existence of such equilibria are provided.

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Jianxing Du, Xifeng Su. 2020-12-31. On the existence of solutions for Frenkel-Kontorova models on quasi-crystals. https://arxiv.org/abs/2012.15594

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