{"paper":{"title":"Optimal convergence rates of the Klein-Gordon-Schr\\\"odinger system in the nonrelativistic limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Weizhu Bao, Yong Lu, Zhiwei Zheng","submitted_at":"2026-07-31T02:33:27Z","abstract_excerpt":"In this paper, we study the Klein-Gordon-Schr\\\"{o}dinger system in the nonrelativistic regime $\\epsilon \\to 0$, where $\\epsilon$ is proportional to the inverse of the speed of light. We show that the Klein-Gordon-Schr\\\"{o}dinger system converges to a system of decoupled linear Schr\\\"odinger equations over a long time interval of order $\\epsilon^{-1}$ with error estimates of the form $(1+t)\\epsilon^2$; in particular, the error estimate for the Schr\\\"odinger component is uniform in time of the form $\\epsilon^{2}$ The specific forms of the error estimates coincide with the numerical results shown"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28963","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/2607.28963/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"}