https://doi.org/10.1140/epjp/s13360-025-06857-1
Regular Article
Modeling and analysis of new rogue wave solutions in a nonlinear left-handed electrical transmission line with the Josephson junction
1
Department of Physics, Higher Teachers’ Training College of Bertoua, The University of
Bertoua, P.O. Box. 416, Bertoua, Cameroon
2
Department of Marine Engineering, Limbé Nautical Arts and Fisheries Institute, P.O Box 485, Limbé, Cameroon
3
Department of Physics, Higher Teachers’ Training College of Bertoua, The University of
Bertoua, P.O. Box. 46, Bertoua, Cameroon
4
Department of Physics, Faculty of Science, The University of Maroua, P.O. Box 814, Maroua, Cameroon
5
Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon
6
Department of Physics, Faculty of Science, The University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
Received:
3
June
2025
Accepted:
16
September
2025
Published online:
24
September
2025
In electrical transmission systems, rogue waves, which are nonlinear phenomena, manifest as sudden and unpredictable voltage and current spikes. In this study, we propose new solution models for rogue waves propagating in a nonlinear electrical transmission line with a Josephson junction. To model the transmission line behavior and analyze the conditions for rogue wave formation, we used an approach based on nonlinear discrete differential equations and the Manakov system, and to formulate the expression for the modulational instability gain spectrum, linear stability was used. Our results show that the Josephson junction and the left-handed nature of this structure play crucial roles in the formation and propagation of these new rogue wave patterns and that the parameters of the Josephson junction and the electrical transmission line can be adjusted to control the occurrence of these phenomena. The Benjamin-Feir instability flourished in the electrical transmission line, and for decreasing the effects of the Josephson junction, the unstable modes increased. We observe an exponential growth of the continuous wave that appears for large values of the perturbed wavenumber, confirming that this structure is open to new coherent localized wave models. We also discuss the implications of our results for the design and management of nonlinear electrical-transmission systems.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
