{"paper":{"title":"Traveling waves in the nonlocal KPP-Fisher equation: different roles of the right and the left interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jana Kopfov\\'a, Karel Hasik, Petra N\\'ab\\v{e}lkov\\'a, Sergei Trofimchuk","submitted_at":"2015-04-27T01:25:18Z","abstract_excerpt":"We consider the nonlocal KPP-Fisher equation $u_t(t,x) = u_{xx}(t,x) + u(t,x)(1-(K *u)(t,x))$ which describes the evolution of population density $u(t,x)$ with respect to time $t$ and location $x$. The non-locality is expressed in terms of the convolution of $u(t, \\cdot)$ with kernel $K(\\cdot) \\geq 0,$ $\\int_{\\mathbb{R}} K(s)ds =1$. The restrictions $K(s), s \\geq 0,$ and $K(s), s \\leq 0,$ are responsible for interactions of an individual with his left and right neighbors, respectively. We show that these two parts of $K$ play quite different roles as for the existence and uniqueness of traveli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06902","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"}