https://doi.org/10.1140/epjp/s13360-023-04195-8
Regular Article
Modulation instability in nonlinear acoustic metamaterials with coupling coefficients
1
Department of Marine Engineering, Limbé Nautical Arts and Fisheries Institute, P.O Box 485, Limbé, Cameroon
2
Department of Basic Science, National Advanced School of Mines and Petroleum Industries, The University of Maroua, P.O Box 08, kaélé, Cameroon
3
Department of Mathematics, Lafayette College, Easton, Pennsylvania, USA
4
Department of Mathematics, Faculty of Science, Firat University, 23119, Elazig, Turkey
5
Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
6
Department of Physics, Faculty of Science, The University of Ngaoundèré, P.O Box 454, Ngaoundèré, Cameroon
a
ahouw220@yahoo.fr
b
abbagaris@yahoo.fr
c
akinyeml@lafayette.edu
Received:
25
April
2023
Accepted:
15
June
2023
Published online:
24
June
2023
In this paper, the modulation instability is analyzed in a novel model of coupled pairs of chains with coupling coefficient parameters. We derive the coupled system of the nonlinear equation by using the Lindstedt–Poincaré perturbation and the multi-scale method. From the linear stability analysis, an expression for the modulation instability growth rate is established, and we assessed the effects of the coupling strength on the modulation instability spectrum in acoustic and optical modes. In acoustic metamaterials, it appears that modulation instability develops and results in the formation of wave trains. We also demonstrated that the modulation instability bandwidth can be reduced or expanded depending on the effectiveness of the coupling coefficient as well as the angular frequency. Through the numerical experiments, we showed the propagation of the modulated wave patterns, manifesting the existence of the modulation instability growth rate in the structure. It results from this investigation that conventional materials where microstructural configurations are designed to exhibit unusual properties are attractive to modulated wave structures. In future works, soliton dynamics, rogue waves, and localized modes will be investigated to give rise to several applications.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
