{"paper":{"title":"Provable bounds for the Korteweg-de Vries reduction in multi-component Nonlinear Schrodinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.MP","nlin.SI","physics.optics"],"primary_cat":"math-ph","authors_text":"Manas Kulkarni, Swetlana Swarup, Vishal Vasan","submitted_at":"2019-08-05T17:59:51Z","abstract_excerpt":"We study the dynamics of multi-component Bose gas described by the Vector Nonlinear Schr\\\"{o}dinger Equation (VNLS), aka the Vector Gross--Pitaevskii Equation (VGPE) . Through a Madelung transformation, the VNLS can be reduced to coupled hydrodynamic equations in terms of multiple density and velocity fields. Using a multi-scaling and a perturbation method along with the Fredholm alternative, we reduce the problem to a Korteweg de-Vries (KdV) system. This is of great importance to study more transparently, the obscure features hidden in VNLS. This ensures that hydrodynamic effects such as disp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02248","kind":"arxiv","version":2},"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/1908.02248/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"}