{"paper":{"title":"Large fronts in nonlocally coupled systems using Conley-Floer homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SG"],"primary_cat":"math.DS","authors_text":"Bente Hilde Bakker, Jan Bouwe van den Berg","submitted_at":"2019-07-08T20:43:03Z","abstract_excerpt":"In this paper we study travelling front solutions for nonlocal equations of the type \\begin{equation} \\partial_t u = N * S(u) + \\nabla F(u), \\qquad u(t,x) \\in \\mathbf{R}^d. \\end{equation} Here $N *$ denotes a convolution-type operator in the spatial variable $x \\in \\mathbf{R}$, either continuous or discrete. We develop a Morse-type theory, the Conley--Floer homology, which captures travelling front solutions in a topologically robust manner, by encoding fronts in the boundary operator of a chain complex. The equations describing the travelling fronts involve both forward and backward delay ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.03861","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"}