{"paper":{"title":"From KP-I lump solution to travelling waves of Gross-Pitaevskii equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Juncheng Wei, Wen Yang, Yong Liu, Zhengping Wang","submitted_at":"2021-10-29T00:19:08Z","abstract_excerpt":"Let $q(x,y)$ be an nondegenerate lump solution to KP-I (Kadomtsev-Petviashvili-I) equation $$\\partial_x^4q-2\\sqrt{2}\\partial_x^2q-3\\sqrt{2}\\partial_x((\\partial_xq) ^2)-2\\partial_y^2q=0. $$ We prove the existence of a traveling wave solution $ u_{\\e} (x-ct, y)$ to GP (Gross-Pitaevskii) equation $$ i\\partial_{t}\\Psi+\\Delta\\Psi+(1-|\\Psi|^{2})\\Psi=0,\\ \\ \\ \\mbox{in} \\ {\\mathbb R}^2 $$ in the transonic limit $$ c=\\sqrt{2}-\\epsilon^2 $$ with $$ u_\\epsilon =1 + i \\epsilon q(x,y) + {\\mathcal O} (\\epsilon^2). $$ This proves the existence of finite energy solutions in the so-called Jones-Roberts program "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.15472","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/2110.15472/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"}