The closeness of the Ablowitz-Ladik lattice to the Discrete Nonlinear Schrödinger equation

While the Ablowitz-Ladik lattice is integrable, the Discrete Nonlinear Schr\"odinger equation, which is more significant for physical applications, is not. We prove closeness of the solutions of both systems in the sense of a "continuous dependence" on their initial data in the l^2 and l^{\infty} metrics. The most striking relevance... Show more