{"paper":{"title":"Prescribing the center of mass of a multi-soliton solution for a perturbed semilinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, M.A. Hamza","submitted_at":"2019-02-13T18:28:56Z","abstract_excerpt":"We construct a finite-time blow-up solution for a class of strongly perturbed semilinear wave equation with an isolated characteristic point in one space dimension. Given any integer $k\\ge 2$ and $\\zeta_0 \\in \\mathbb{R}$, we construct a blow-up solution with a characteristic point $a$, such that the asymptotic behavior of the solution near $(a,T(a))$ shows a decoupled sum of $k$ solitons with alternate signs, whose centers (in the hyperbolic geometry) have $\\zeta_0$ as a center of mass, for all times. Although the result is similar to the unperturbed case in its statement, our method is new. I"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05051","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"}