45 citations · 162 across the 29 of their papers we have counts for
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Bounds on the tight-binding approximation for the Gross-Pitaevskii equation with a periodic potential
Dmitry Pelinovsky, Guido Schneider
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…
Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential
Tomas Dohnal, Dmitry Pelinovsky, Guido Schneider
We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the f…
Moving gap solitons in periodic potentials
Dmitry Pelinovsky, Guido Schneider
We address existence of moving gap solitons (traveling localized solutions) in the Gross-Pitaevskii equation with a small periodic potential. Moving gap solitons are approximated b…
Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential
Dmitry Pelinovsky, Guido Schneider
Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized s…