https://doi.org/10.1140/epjp/s13360-023-04145-4
Regular Article
Dynamics of Rogue waves in one-dimensional acoustic transmission line metamaterials
1
Department of Physics, Faculty of Science, The University of Maroua, P.O. Box. 814, Maroua, Cameroon
2
Higher Teachers’ Training College of Maroua, The University of Maroua, P.O. Box. 55, Maroua, Cameroon
3
National Advanced School of Engineering, The University of Maroua, P.O. Box 46, Maroua, Cameroon
4
Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
5
Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey
6
Department of Medical Research, China Medical University, 40402, Taichung, Taiwan
Received:
8
October
2022
Accepted:
23
May
2023
Published online:
6
July
2023
Analytically, modulational instability phenomenon and Rogue wave propagation are studied in an acoustic metamaterial based on the one-dimensional transmission line approach. Kirchhoff’s pressure and volume velocity laws for two successive cells and the multiple scales method allowed the determination of coupled nonlinear Schrödinger equations. By applying the disturbance method in amplitude to the coupled nonlinear Schrödinger equations, the modulational instability gain is obtained, and its curves are plotted. The similarity technique combined with the first- and second-order rational solutions of the one-dimensional Manakov system, which serve as prototypes of rogue wavelike solutions, is used to illustrate the dynamics of Rogue waves in the proposed model. The role and interplay between nonlinearity, dispersion, and diffraction parameters are investigated on the modulational instability gain and formation of Rogue waves. The results indicate that the modulational instability gain and Rogue wave intensities depend on the radius, thickness, and distance between the two plates of the proposed acoustic metamaterial model. To design such metamaterials, these parameters can be considered to minimize the damage caused by the dynamics of Rogue waves. The present results are innovative and have interesting applications in the engineering sciences.
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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.
