{"paper":{"title":"On the derivation of the wave kinetic equation for NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Yu Deng, Zaher Hani","submitted_at":"2019-12-19T19:45:48Z","abstract_excerpt":"A fundamental question in wave turbulence theory is to understand how the \"wave kinetic equation\" (WKE) describes the long-time dynamics of its associated nonlinear dispersive equation. Formal derivations in the physics literature date back to the work of Pieirls in 1928. For the cubic nonlinear Schr\\\"odinger equation, it is expected that such a kinetic description should hold, in a limiting regime where the size $L$ of the domain goes to infinity, and the strength $\\alpha$ of the nonlinearity goes to 0 (weak nonlinearity), at a kinetic time scale $T_{\\mathrm{kin}}=O(\\alpha^{-2})$.\n  In this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.09518","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/1912.09518/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"}