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arXiv · 0711.2694

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

Dmitry Pelinovsky·Guido Schneider
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Abstract

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. Our construction of the periodic potential and the associated Wannier functions is based on the previous work, while our analysis involving energy estimates and Gronwall's inequality addresses time-dependent localized solutions on large but finite time intervals.

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Dmitry Pelinovsky, Guido Schneider. 2007-11-16. Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential. https://arxiv.org/abs/0711.2694

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