{"paper":{"title":"Complete Weierstrass elliptic function solutions for coherent couplers and their relation to degenerate four-wave mixing","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Graham Hesketh","submitted_at":"2026-05-19T00:41:23Z","abstract_excerpt":"Complete analytic solutions for the coherent coupler with arbitrary propagation constants and self- and cross-phase modulation coefficients are presented in terms of Weierstrass elliptic $\\wp$, $\\zeta$, and $\\sigma$ functions, giving the full complex envelopes for both modes under generic initial conditions. Jensen's coupler emerges as a special case of the general system. The mode solutions contain factors of the form $\\exp(r\\log R(z))$, where $R(z)$ is a ratio of Weierstrass $\\sigma$ functions, giving a multi-valued branch structure that is removable by a gauge transformation. A projection f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19216","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/2605.19216/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"}