The fractional nonlinear magnetoinductive impurity

Mario I. Molina

Chaos, Solitons & Fractals, 2025, vol. 191, issue C

Abstract: We study a one-dimensional split-ring resonator array containing a single linear/nonlinear magnetic impurity where the usual discrete Laplacian is replaced by a fractional one. In the absence of the impurity, the dispersion relation for magnetoinductive waves is obtained in closed form, with a bandwidth that decreases with a decrease in the fractional exponent. Next, by using lattice Green functions, we obtain the bound state energy and its spatial profile, as a function of the impurity strength. We demonstrate that, at large impurity strengths, the bound state energy becomes linear with impurity strength for both linear and nonlinear impurity cases. The transmission of plane waves is computed semi-analytical, showing a qualitative similarity between the linear and nonlinear impurity cases. Finally, we compute the amount of magnetic energy remaining at the impurity site after evolving the system from a completely initially localized condition at the impurity site. For both cases, linear and nonlinear impurities, it is found that for a fixed fractional exponent, there is trapping of magnetic energy, which increases with an increase in impurity strength. The trapping increases with a decreased fractional exponent for a fixed magnetic strength.

Keywords: Fractional; Nonlinear; Magnetoinductive; Impurity (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924013262
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:191:y:2025:i:c:s0960077924013262

DOI: 10.1016/j.chaos.2024.115774

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().