https://doi.org/10.1140/epjp/s13360-025-06124-3
Regular Article
Next-next-nearest neighbor hopping effects on the MI and on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices
1
Unité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Fotso Victor University Institute of Technology, University of Dschang, P.O. Box 134 , Bandjoun, Cameroon
2
Pure physics laboratory: Group of Nonlinear physics and Complex systems, Department of Physics, University of Douala, P.O. Box 24157, Douala, Cameroon
3
The African Institute for Mathematical Sciences (AIMS), 6 Melrose Road, Muizenberg, 7945, Cape Town, South Africa
4
Nonlinear physics and Complex systems, Department of Physics, The Higher Teachers’ Training College, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon
a djoufackzacharie@yahoo.fr, isidore.djoufack@univ-dschang.org
Received:
27
November
2024
Accepted:
12
February
2025
Published online:
25
February
2025
We explore analytically and numerically the dual role played by the next-next-nearest neighbor (NNNN) hopping coupling on the modulation instability (MI) and on the dynamics of breathers in 2D quantum ultracold atoms loaded in optical lattices. Via the linear stability analysis, it is shown that the dispersion relation formed exhibits intriguing forms. It is found that the emergence of MI regions and the growth rate may be significantly affected by the NNNN hopping coupling strength. To support the analytical studies, direct numerical simulations of MI are carried out to show the generation of a train of short waves exhibiting periodic W-shaped and V-shaped solitons with decreasing amplitude as time evolves. The appearance of breathers in the regions where the MI manifests is predicted to be influenced by the NNNN hopping coupling strength. By making use of Rayleigh-Ritz variational approach and in agreement with the MI analysis, the analytical results reveal the existence of the radial modes and discrete vortex solitons in called this framework, the dynamics of breathers. The accuracy of the outcomes is checked by numerical calculations which show a good agreement with the theoretical analysis.
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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.
