{"paper":{"title":"Nonlinear Schr\\\"{o}dinger equation on a closed 3D elastica knot","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MP","physics.plasm-ph"],"primary_cat":"math-ph","authors_text":"Alain J. Brizard","submitted_at":"2026-07-23T19:04:11Z","abstract_excerpt":"An elastica knot is defined in terms of the Frenet-Serret curvature $\\kappa(s,t)$ as a function of the arclength $s$ along the spatial curve ${\\bf r}(s,t)$ at a fixed time $t$, which is a solution of the curvature differential equation $\\partial^{2}_{s}\\kappa(s,t) = -\\;\\kappa^{3}/2 + k_{0}^{4}\\tau_{0}^{2}\\;\\kappa^{-3} + \\lambda\\,k_{0}^{2}\\kappa/2$ that is obtained from a variational principle that minimizes the bending energy of the spatial curve under the constraint of a constant curve length. Here, the Frenet-Serret torsion $\\tau(s,t)$ satisfies the conservation law $\\kappa^{2}(s,t)\\,\\tau(s,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21750","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/2607.21750/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"}