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 ⊂<!-- ⊂ --> R 3 G⊂ R^3 such that for every <tex-math> k∈ G</tex-math> there is a solution asymptotically close to a plane wave <tex-math> Ae^{i {k}, {x} }</tex-math> as <tex-math> | k|→ ∞ </tex-math>, given A A is sufficiently small.