{"paper":{"title":"An algebraic-geometric construction of \"lump\" solutions of the KP1 equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.AG","authors_text":"John B. Little","submitted_at":"2024-04-23T16:35:46Z","abstract_excerpt":"In this note, we show how certain everywhere-regular real rational function solutions of the KP1 equation (\"multi-lumps\") can be constructed via the polynomial analogs of theta functions from singular rational curves with cusps. We use two methods, one direct and the other producing a degeneration of the well-understood soliton solutions from nodal singular curves. The second approach can be seen as a variation on the long-wave limit technique of Ablowitz and Satsuma, as developed by Zhang, Yang, Li, Guo, and Stepanyants. We present an explicit example of a three-lump solution constructed via "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.15200","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/2404.15200/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"}