Numerical and Analytical Investigation of the Ablowitz–Ladik and Salerno Models: Closeness to Cubic and Cubic‐Quintic Discrete Nonlinear Schrödinger Lattices

We study the closeness between the Ablowitz–Ladik, Salerno, and discrete nonlinear Schrödinger lattices in regimes of small coupling \epsilon
and small energy norm \rho. Two approaches are compared: direct estimates in physical variables and a transformation to canonical symplectic coordinates via Darboux variables. Our analytical results provide bounds on the distance between solutions of these models over natural and extended time scales. Numerical simulations identify a threshold \epsilon^* ~ \rho^2 that separates weakly coupled and dispersive regimes, suggesting a good level of sharpness for our estimates below such a threshold, and reveal slower growth of the distance than predicted analytically for \epsilon > \epsilon^*.