{"paper":{"title":"Entire Solutions of Diffusive Lotka-Volterra System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"King-Yeung Lam, Qiliang Wu, Rachidi B. Salako","submitted_at":"2020-02-02T03:05:57Z","abstract_excerpt":"This work is concerned with the existence of entire solutions of the diffusive Lotka-Volterra competition system \\begin{equation}\\label{eq:abstract} \\begin{cases} u_{t}= u_{xx} + u(1-u-av), & \\qquad \\ x\\in\\mathbb{R} \\cr v_{t}= d v_{xx}+ rv(1-v-bu), & \\qquad \\ x\\in\\mathbb{R} \\end{cases} \\quad (1) \\end{equation} where $d,r,a$, and $b$ are positive constants with $a\\neq 1$ and $b\\neq 1$. We prove the existence of some entire solutions $(u(t,x),v(t,x))$ of $(1)$ corresponding to $(\\Phi_{c}(\\xi),0)$ at $t=-\\infty$ (where $\\xi=x-ct$ and $\\Phi_c$ is a traveling wave solution of the scalar Fisher-KPP "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.00308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.00308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}