{"paper":{"title":"x-periodic Quasi One Dimensional Anomalous (Rogue) Waves in Multidimensional Nonlinear Schr\\\"odinger Equations: Fission, Fusion, and Recurrence","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.PS","authors_text":"Francesco Coppini, Paolo Maria Santini","submitted_at":"2026-05-26T12:51:05Z","abstract_excerpt":"In a recent work we studied the first nonlinear stage of modulation instability (NLSMI) of x-periodic anomalous (rogue, freak, extreme) waves (AWs) of physically relevant multidimensional (generalizations of the focusing) nonlinear Schr\\\"odinger (MNLS) equation, like the non integrable elliptic and hyperbolic nonlinear Schr\\\"odinger (NLS) equations in d+1 dimensions, d = 2, 3, in the quasi one dimensional (Q1D) regime in which the wavelength in the direction of propagation x is small with respect to the wavelengths in the transversal directions. We showed that, at leading order, the first NLSM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26961","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/2605.26961/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"}