{"paper":{"title":"Effective dynamics of the nonlinear Schr\\\"odinger equation on large domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jalal Shatah, Pierre Germain, Tristan Buckmaster, Zaher Hani","submitted_at":"2016-10-12T18:59:06Z","abstract_excerpt":"We consider the nonlinear Schr\\\"odinger (NLS) equation posed on the box $[0,L]^d$ with periodic boundary conditions. The aim is to describe the long-time dynamics by deriving effective equations for it when $L$ is large and the characteristic size $\\epsilon$ of the data is small. Such questions arise naturally when studying dispersive equations that are posed on large domains (like water waves in the ocean), and also in theory of statistical physics of dispersive waves, that goes by the name of \"wave turbulence\". Our main result is deriving a new equation, the continuous resonant (CR) equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03824","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":""},"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"}