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

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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.

publication date

  • February 2010