170 citations · 491 across the 31 of their papers we have counts for
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math.AP2007★ 25 cited
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…
math.AP2007★ 14 cited
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…
math.AP2007★ 24 cited
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…