{"paper":{"title":"Solutions of Gross-Pitaevskii Equation with Periodic Potential in Dimension Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Roman Shterenberg, Seonguk Kim, Yulia Karpeshina","submitted_at":"2018-05-08T22:10:59Z","abstract_excerpt":"Quasi-periodic solutions of a nonlinear polyharmonic equation for the case $4l>n+1$ in $\\R^n$, $n>1$, are studied. This includes Gross-Pitaevskii equation in dimension two ($l=1,n=2$). It is proven that there is an extensive \"non-resonant\" set ${\\mathcal G}\\subset \\R^n$ such that for every $\\vec k\\in \\mathcal G$ there is a solution asymptotically close to a plane wave $Ae^{i\\langle{ \\vec{k}, \\vec{x} }\\rangle}$ as $|\\vec k|\\to \\infty $, given $A$ is sufficiently small."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03974","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}