{"paper":{"title":"Existence of breathing patterns in globally coupled finite-size nonlinear lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Dirk Hennig","submitted_at":"2014-04-10T07:23:40Z","abstract_excerpt":"We prove the existence of time-periodic solutions consisting of patterns built up from two states, one with small amplitude and the other one with large amplitude, in general nonlinear Hamiltonian finite-size lattices with global coupling. Utilising the comparison principle for differential equations it is demonstrated that for a two site segment of the nonlinear lattice one can construct solutions that are sandwiched between two oscillatory localised lattice states. Subsequently, it is proven that such a localised state can be embedded in the extended nonlinear lattice forming a breathing pat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2712","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":""},"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"}