https://doi.org/10.1140/epjp/s13360-023-04773-w
Regular Article
Dynamics of rogue waves and modulational instability with the Manakov system in a nonlinear electric transmission line with second couplings
1
Department of Physics, Higher Teachers’ Training College of Bertoua, The University of Bertoua, P.O. Box 416, Bertoua, Cameroon
2
Department of Physics, Faculty of Science, The University of Maroua, P.O. Box 814, Maroua, Cameroon
3
Department of Physics, Higher Teachers’ Training College of Maroua, 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 Physics, Faculty of Science, The University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
Received:
20
June
2023
Accepted:
3
December
2023
Published online:
15
December
2023
In this study, we investigate rogue wave dynamics and modulational instability using the Manakov system in a nonlinear electrical transmission line with second couplings. Using semi-discrete approximation, we demonstrate how the dynamics of rogue waves in this type of transmission line can be governed by the Manakov system. To study the dynamics of rogue waves in this structure via this approximation, we used the parameters of this transmission line and derived new forms of propagating rogue wave solutions. The solutions obtained are presented as new rogue waves of types I and II. In this work, we show that the dynamics of different types of rogue waves in different types of nonlinear electrical transmission lines can be studied using the Manakov system. Indeed, with the choice of small values of inductance in the two types of rogue waves, the effects of the second coupling are clearly visible during the formation of these waves, namely at the level shapes, hollows, and amplitude. Additionally, it can be observed that the dispersion capacity also affects the shapes, troughs, peaks, and widths of these rogue waves as the troughs gradually disappear, and the peak widths decrease when the dispersion capacity increases. Finally, concerning the modulational instability in this structure, the essential information that we can retain is that these second couplings would impact the zones of instability, which could gradually disappear along this line. To avoid overload, we limited ourselves to these major effects. The results obtained by this Manakov system show not only its efficiency and robustness, but also its potential applicability to other types of useful nonlinear electrical transmission lines, and that these new forms of rogue waves do indeed exist in nonlinear electrical transmission lines with second couplings. This feature has not been sufficiently addressed in this type of nonlinear electrical transmission line and will be useful in many branches of physics.
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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.