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In this paper, we consider the nonlinear one-dimensional time-dependent Schrödinger equation with a periodic potential and a bounded perturbation. In the limit of large periodic potential, the time behavior of the wavefunction can be approximated, with a precise estimate of the remainder term, by means of the solution to the discrete nonlinear Schrödinger equation of the tight-binding model.

Derivation of the Tight-Binding Approximation for Time-Dependent Nonlinear Schrödinger Equations