{"paper":{"title":"Stationary solutions for the nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"Benedetta Ferrario, Margherita Zanella","submitted_at":"2023-05-17T17:33:55Z","abstract_excerpt":"We construct stationary statistical solutions of a deterministic unforced nonlinear Schr\\\"odinger equation, by perturbing it by a linear damping $\\gamma u$ and a stochastic force whose intensity is proportional to $\\sqrt \\gamma$, and then letting $\\gamma\\to 0^+$. We prove indeed that the family of stationary solutions $\\{U_\\gamma\\}_{\\gamma>0}$ of the perturbed equation possesses an accumulation point for any vanishing sequence $\\gamma_j\\to 0^+$ and this stationary limit solves the deterministic unforced nonlinear Schr\\\"odinger equation and is not the trivial zero solution. This technique has b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.10393","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.10393/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}