Wave propagation in discrete cold bosonic atoms zig-zag optical lattice

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.