Analytical solutions of the discrete nonlinear Schrödinger equation in arrays of optical fibers

We find the analytical solutions of the discrete nonlinear Schrödinger equation which models arrays of optical fibers according to the fact that the signal which propagate in the fiber under consideration of the array can be prone to the lateness or accelerating effects of the neighbouring fibers. Firstly, we give the recurrence relation which governs the number of fiber “n”and secondly, we apply the projective Riccati method to achieve the resolution.