{"paper":{"title":"Solutions of Fixed Period in the Nonlinear Wave Equation on Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Garc\\'ia-Azpeitia, Wieslaw Krawcewicz, Yanli Lv","submitted_at":"2018-04-28T13:45:04Z","abstract_excerpt":"The wave equation on network is defined by $\\partial_{tt}u=\\Delta_{G}u+g(u)$, where $u\\in\\mathbb{R}^{n}$ and the graph Laplacian $\\Delta_{G}$ is an operator on functions on $n$ vertices. We suppose that $g:\\mathbb{R}^{n}\\rightarrow \\mathbb{R}^{n}$ is an odd continuous function that satisfies $g(0)=g^{\\prime }(0)=0$ and the Nagumo condition. Assuming that the graph is invariant by a subgroup of permutations $\\Gamma$, using a $\\Gamma$-equivariant topological invariant we prove the existence of multiple non-constant $p$-periodic solutions characterized by their symmetries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10803","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"}