Solutions of gross-pitaevskii equation with periodic potential in dimension three

Quasiperiodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proved that there is an extensive "nonresonant" set G subset of R-3 such that for every k(->) is an element of G there is a solution asymptotically close to a plane wave Ae(i) (k(->), x(->)) as |k(->)| -> infinity, given A is sufficiently small.