{"paper":{"title":"GBDT with nontrivial seeds: explicit solutions of the focusing NLS equations and the corresponding Weyl functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Alexander Sakhnovich","submitted_at":"2025-06-09T12:41:26Z","abstract_excerpt":"Our GBDT (generalised B\\\"acklund-Darboux transformation) approach is used to construct explicit solutions of the focusing nonlinear Schr\\\"odinger (NLS) equation in the case of the exponential seed $a \\exp\\{2 i (cx +dt)\\}$. The corresponding Baker-Akhiezer functions and evolution of the Weyl functions are obtained as well. In particular, the solutions, which appear in the study of rogue waves, step-like solutions and $N$-modulation solutions of the NLS equation are considered. This work is an essential development of our joint work with Rien Kaashoek and Israel Gohberg, where the seed was trivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07702","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/2506.07702/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"}