D. Pelinovsky and G. Schneider

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

Journal of Differential Equations 248, 837-849 (2010)

We justify the validity of the discrete nonlinear Schrodinger 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, this work deals with time-dependent space-decaying solutions on large but finite time intervals.

justification of amplitude equations, gap solitons in periodic potentials, Gross-Pitaevskii equation, Fourier-Bloch decomposition, Wannier functions, discrete nonlinear Schrodinger equation