{"paper":{"title":"A Floer homology approach to travelling waves in reaction-diffusion equations on cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SG"],"primary_cat":"math.DS","authors_text":"Bente Bakker, Jan Bouwe van den Berg, Rob Vandervorst","submitted_at":"2017-02-02T18:22:19Z","abstract_excerpt":"We develop a new homological invariant for the dynamics of the bounded solutions to the travelling wave PDE \\[ \\left\\{ \\begin{array}{l l}\n  \\partial_t^2 u - c \\partial_t u + \\Delta u + f(x,u) = 0 \\qquad & t \\in \\mathbf{R},\\; x \\in \\Omega, \\newline\n  B(u) = 0 & t \\in \\mathbf{R},\\; x \\in \\partial \\Omega, \\end{array} \\right. \\] where $c \\neq 0$, $\\Omega \\subset \\mathbf{R}^d$ is a bounded domain, $\\Delta$ is the Laplacian on $\\Omega$, and $B$ denotes Dirichlet, Neumann, or periodic boundary data. Restrictions on the nonlinearity $f$ are kept to a minimum, for instance, any nonlinearity exhibiting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00772","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"}