Journal of Theoretical, Experimental, and Applied Physics
Second-Neighbor Hopping Effects on the Dynamics of Breathers in 2D Quantum Ultracold Atoms Loaded in Optical Lattices
Abstract
Z I Djoufack, J P Nguenang and A Kenfack Jiotsa
We explore analytically and numerically the dual role played by the second-neighbor hopping on the modulation instability 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 existence conditions of appearance of the modulational instability (MI) regions and the growth rate may be significantly affected by the second neighbor hopping coupling strength. To support the analytical studies, direct numerical simulations of MI is 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 emergence of breathers in the regions where the MI manifests is predicted to be influenced by the second neighbor hopping coupling strength. By making use of Rayleigh-Ritz variational method and in agreement with the MI analysis, the analytical results reveal the existence of the radial symmetric modes called the dynamics of breathers. The accuracy of the outcomes is checked by numerical calculations which show a good agreement with the theoretical analysis.
