Propagation of envelope bright breather coupled wave modes in Ablowitz-Ladik chains

We investigate a model of a two coupled Ablowitz-Ladik (AL) lattices which admits the integrable AL model, when it is reduced to symmetric states. We compute the discrete modulational instability gain analytically and verified numerically. The play-role of the coupling parameter ϵ which is the back-bone of the two coupled AL chain is analyzed. We perform molecular dynamics (MD) simulations and elucidate the short time as well as the long time instability of AL chain. We demonstrate that the AL chain supports the formation of bright breather coupled wave modes spanning over 36 lattice sites on either side of the bond-center. We explore a kink solitary profile of solutions for the AL chains by invoking the extended tangent hyperbolic function method (ETHF) embedded with symbolic computation. Spectral stability of the exact solutions is determined by the eigenvalues of the discrete spectrum. We demonstrate the onset of chaos that leads the quasi-periodic dynamics of AL chains through the period-doubling bifurcation route to chaos.