{"paper":{"title":"On the B\\\"acklund transform and the stability of the line soliton of the KP-II equation on $\\mathbb R^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lorenzo Pompili","submitted_at":"2024-12-17T04:40:56Z","abstract_excerpt":"We study the Miura map of the KP-II equation on $\\mathbb R^2$ and the resulting B\\\"acklund transform, which adds a line soliton to a given solution. This work aims to develop a complementary approach to T. Mizumachi's method for the $L^2$-stability of the line soliton, which the potential for generalization to multisolitons. We construct the B\\\"acklund transform by classifying solutions of the Miura map equation close to a modulated kink; this translates into studying eternal solutions of the forced viscous Burgers' equation under distinct boundary conditions at $\\pm\\infty$. We then show that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.12530","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/2412.12530/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"}