{"paper":{"title":"Bifurcations of nontrivial solutions of a cubic Helmholtz system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dominic Scheider, Rainer Mandel","submitted_at":"2018-11-02T09:14:41Z","abstract_excerpt":"This paper presents local and global bifurcation results for radially symmetric solutions of the cubic Helmholtz system \\begin{equation*} \\begin{cases} -\\Delta u - \\mu u = \\left( u^2 + b \\: v^2 \\right) u &\\text{ on } \\mathbb{R}^3, \\\\ -\\Delta v - \\nu v = \\left( v^2 + b \\: u^2 \\right) v &\\text{ on } \\mathbb{R}^3. \\end{cases} \\end{equation*} It is shown that every point along any given branch of radial semitrivial solutions $(u_0, 0, b)$ or diagonal solutions $(u_b, u_b, b)$ (for $\\mu = \\nu$) is a bifurcation point. Our analysis is based on a detailed investigation of the oscillatory behavior of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00789","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"}