{"paper":{"title":"Stability of the line soliton of the Kadomtsev--Petviashvili-I equation with the critical traveling speed","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yohei Yamazaki","submitted_at":"2017-10-27T13:07:57Z","abstract_excerpt":"We consider the orbital stability of solitons of the Kadomtsev--Petviashvili-I equation in $\\mathbb{R} \\times (\\mathbb{R}/2\\pi\\mathbb{Z})$ which is one of a high dimensional generalization of the Korteweg--de Vries equation. Benjamin showed that the Korteweg--de Vries equation possesses the stable one soliton. We regard the one soliton of the Korteweg--de Vries equation as a line soliton of the Kadomtsev--Petviashvili-I equation. Zakharov and Rousset--Tzvetkov proved the orbital instability of the line solitons of the Kadomtsev--Petviashvili-I equation on $\\mathbb{R}^2$. In the case of the Kad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10115","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":""},"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"}