{"paper":{"title":"On the final-state problem for the 1D cubic NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gong Chen, Yongyu Qiang","submitted_at":"2026-05-21T21:54:40Z","abstract_excerpt":"We consider the one-dimensional cubic nonlinear Schr\\\"odinger equation $$ \\ii\\partial_tu+\\frac12\\partial_{xx}u=\\la|u|^2u,\\,\\lambda=\\pm 1 $$ and solve the final-state (modified wave operator) problem for small asymptotic data. More precisely, given a small $W(\\xi)$, we construct a solution $u$ such that \\begin{equation*}\n  u\\rightarrow (2\\pi)^{-1/2}(\\ii t)^{-1/2}e^{\\ii x^2/(2t)}\\, W\\!\\Big(\\frac{x}{t}\\Big)\\exp(-\\ii\\la|W(x/t)|^2\\log t). \\end{equation*} Crucially, we design a contraction map, so that we can run the analysis in the spirit of Kato--Pusateri \\cite{KP} for $w$ with a forcing term depe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23063","kind":"arxiv","version":1},"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/2605.23063/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"}