Discrete Solitons and Backlund Transformation for the Coupled Ablowitz- Ladik Equations

Under investigation in this paper are the coupled Ablowitz-Ladik equations, which are linked to the optical fibres, waveguide arrays, and optical lattices. Binary Bell polynomials are applied to construct the bilinear forms and bilinear Backlund transformation. Bright/dark one-and two-soliton solutions are also obtained. Asymptotic analysis indicates that the interactions between the bright/dark two solitons are elastic. Amplitudes and velocities of the bright solitons increase as the value of the lattice spacing increases. Increasing value of the lattice spacing can lead to the increase of both the bright solitons' amplitudes and velocities, and the decrease of the velocities of the dark solitons. The lattice spacing parameter has no effect on the amplitudes of the dark solitons. Overtaking interaction between the unidirectional bright two solitons and a bound state of the two equal-velocity solitons is presented. Overtaking interaction between the unidirectional dark two solitons and the two parallel dark solitons is also plotted.