{"paper":{"title":"The initial-value problem for the cubic-quintic NLS with non-vanishing boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jason Murphy, Monica Visan, Rowan Killip","submitted_at":"2017-02-14T22:52:47Z","abstract_excerpt":"We consider the initial-value problem for the cubic-quintic NLS \\[ (i\\partial_t+\\Delta)\\psi=\\alpha_1 \\psi-\\alpha_{3}\\vert \\psi\\vert^2 \\psi+\\alpha_5\\vert \\psi\\vert^4 \\psi \\] in three spatial dimensions in the class of solutions with $|\\psi(x)|\\to c >0$ as $|x|\\to\\infty$. Here $\\alpha_1$, $\\alpha_3$, $\\alpha_5$ and $c$ are such that $\\psi(x)\\equiv c$ is an energetically stable equilibrium solution to this equation. Normalizing the boundary condition to $\\psi(x)\\to 1$ as $|x|\\to\\infty$, we study the associated initial-value problem for $u=\\psi-1$ and prove a scattering result for small initial da"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04413","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"}