{"paper":{"title":"On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Athanasios Stylianou, Yongming Luo","submitted_at":"2019-02-14T20:16:33Z","abstract_excerpt":"We study the following nonlocal mixed order Gross-Pitaevskii equation $$i\\,\\partial_t \\psi=-\\frac{1}{2}\\,\\Delta \\psi+V_{ext}\\,\\psi+\\lambda_1\\,|\\psi|^2\\,\\psi+\\lambda_2\\,(K*|\\psi|^2)\\,\\psi+\\lambda_3\\,|\\psi|^{p-2}\\,\\psi,$$ where $K$ is the classical dipole-dipole interaction kernel, $\\lambda_3>0$ and $p\\in(4,6]$; the case $p=6$ being energy critical. For $p=5$ the equation is considered currently as the state-of-the-art model for describing the dynamics of dipolar Bose-Einstein condensates (Lee-Huang-Yang corrected dipolar GPE). We prove existence and nonexistence of standing waves in different p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05591","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"}