https://doi.org/10.1140/epjp/s13360-024-04961-2
Regular Article
Modulation instability spectrum and rogue waves of the repulsive lattices
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, Hampton University, Hampton, VA, USA
4
Department of Physics, Faculty of Science, The University of Ngaoundéré, P.O. Box 454, Ngaoundéré, Cameroon
a
ahouw220@yahoo.fr
b
abbagaris@yahoo.fr
c
lanre.akinyemi@hamptonu.edu
Received:
25
September
2023
Accepted:
31
January
2024
Published online:
19
February
2024
In this work, the modulation instability and solitonic rogue waves are addressed in the repulsive lattice formed by identical particles with nearest neighbor couplings. We use the multiple scale method to derive the extended nonlinear Schrödinger equation with fourth-order dispersion and cubic–quintic nonlinearity. To calculate the modulation instability growth rate, a linear stability analysis is used. Thereafter, we have demonstrated that both fourth-order dispersion and quintic nonlinearity can change the amplitude of the plane wave and bandwidth of the modulation instability in normal and anomalous dispersion regimes. The dynamics of the solitonic rogue waves have been pointed out to show an increasing amplitude with the variation of the free amplitude parameter of the chain of magnets. Via the numerical simulation, the modulated wave patterns have been exhibited to manifest the development of the modulation instability spectrum in the lattice, and the long-time evolution of the continuous waves has brought new features to show an increasing amplitude of the trains of pulses under the variation of the interaction interatomic parameters. These parameters are revealed to be a suitable tool to manipulate nonlinear objects in nonlinear media where higher-order dispersion competes with nonlinearity.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.