{"paper":{"title":"On the asymptotic reduction to the multidimensional nonlinear Schrodinger equation","license":"","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"M.M.Shakir'yanov (Institute of Mathematics, Russian Academy of Sciences), Ufa Scientific Center","submitted_at":"1999-07-02T11:27:29Z","abstract_excerpt":"The problem on the asymptotics for the solution of multidimensional nonlinear Boussinesq equation with respect to a small parameter $\\ve$ is considered. The asymptotic expansion of the solution of this problem with respect to $\\ve\\to0$ for long times $t\\sim {\\cal O}(\\ve^{-2})$ is constructed and justified. The leading terms of the asymptotic solution are defined from the multidimensional nonlinear Schrodinger equation and from the linear homogeneous wave equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9907003","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/math-ph/9907003/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"}