{"paper":{"title":"Construction of multi-bubble solutions for the critical gKdV equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Vianney Combet, Yvan Martel","submitted_at":"2017-06-29T17:34:54Z","abstract_excerpt":"We prove the existence of solutions of the mass critical generalized Korteweg-de Vries equation $\\partial_t u + \\partial_x(\\partial_{xx} u + u^5) = 0$ containing an arbitrary number $K\\geq 2$ of blow up bubbles, for any choice of sign and scaling parameters: for any $\\ell_1>\\ell_2>\\cdots>\\ell_K>0$ and $\\epsilon_1,\\ldots,\\epsilon_K\\in\\{\\pm1\\}$, there exists an $H^1$ solution $u$ of the equation such that \\[ u(t) - \\sum_{k=1}^K \\frac {\\epsilon_k}{\\lambda_k^\\frac12(t)} Q\\left( \\frac {\\cdot - x_k(t)}{\\lambda_k(t)} \\right) \\longrightarrow 0 \\quad\\mbox{ in }\\ H^1 \\mbox{ as }\\ t\\downarrow 0, \\] with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09870","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"}