{"paper":{"title":"Construction of multi solitary waves with symmetry for the damped nonlinear Klein-Gordon equation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haiming Du, Rapha\\\"el C\\^ote","submitted_at":"2024-11-18T16:30:19Z","abstract_excerpt":"We are interested in the nonlinear damped Klein-Gordon equation \\[ \\partial_t^2 u+2\\alpha \\partial_t u-\\Delta u+u-|u|^{p-1}u=0 \\] on $\\mathbb{R}^d$ for $2\\le d\\le 5$ and energy sub-critical exponents $2 < p < \\frac{d+2}{d-2}$.\n  We construct multi-solitons, that is, solutions which behave for large times as a sum of decoupled solitons, in various configurations with symmetry: this includes multi-solitons whose soliton centers lie at the vertices of an expanding regular polygon (with or without a center), of a regular polyhedron (with a center), or of a higher dimensional regular polytope. We g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11703","kind":"arxiv","version":2},"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/2411.11703/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"}