Wave propagation in discrete cold bosonic atoms zig–zag optical lattice
Department of Marine Engineering, Limbe Nautical Arts and Fisheries Institute, P.O Box 485, Limbe, Cameroon
2 Department of Physics, Faculty of Science, University of Maroua, P.O Box 814, Maroua, Cameroon
3 Department of Basic Science, National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O Box 08, kaélé, Cameroon
4 Department of Mathematics, Lafayette College, Easton, PA, USA
5 Department of Computer Engineering, Biruni University, Istanbul, Turkey
6 Department of Mathematics, Science Faculty, Firat University, 23119, Elazig, Turkey
7 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
8 Department of Physics, Faculty of Science, University of Ngaoundéré, P.O Box 454, Ngaoundéré, Cameroon
Accepted: 25 August 2022
Published online: 10 September 2022
In this paper, we investigated the propagation of the modulated waves patterns in the cold bosonic atom zig–zag optical array where the first nearest neighbor and second nearest neighbor (SNN) are considered. We pointed out the forward and backward wave propagation and its unstable/stable zones. The effects of the NNs on modulation instability growth rate and MWs patterns have been highlighted. This analysis shows that the SNN can induce unstable zones from where the bullets appear. By considering the linear analysis, we have shown lower and upper gaps from where the group velocity vanishes and open the way to the nonlinear supratransmission matter. To get to this phenomenon, we have submitted one end of the lattice to the external harmonic forcing. Thus, we establish the expression of the threshold amplitude which is linked to the static breather. We have shown the propagation of bright soliton with the variation of the driven amplitude (DA). It results that nonlinear energy localization happening and BS acquires novel features for a large value of the DA. We can predict that the SNN and the DA are sources of energy for cold bosonic atoms in the zig–zag optical lattices.
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