Bounds on the tight-binding approximation for the Gross–Pitaevskii equation with a periodic potential

We justify the validity of the discrete nonlinear Schrödinger equation for the tight-binding approximation in the context of the Gross–Pitaevskii equation with a periodic potential. Both piecewise-constant and smooth potentials are considered in the semi-classical limit. While justification of stationary equations is developed in our previous work (Pelinovsky et al. (2008) [11]), this work deals with time-dependent space-decaying solutions on large but finite time intervals.