{"paper":{"title":"Detection of Hermitian connections in wave equations with cubic non-linearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gabriel P. Paternain, Lauri Oksanen, Matti Lassas, Xi Chen","submitted_at":"2019-02-15T07:45:23Z","abstract_excerpt":"We consider the geometric non-linear inverse problem of recovering a Hermitian connection $A$ from the source-to-solution map of the cubic wave equation $\\Box_{A}\\phi+\\kappa |\\phi|^{2}\\phi=f$, where $\\kappa\\neq 0$ and $\\Box_{A}$ is the connection wave operator in the Minkowski space $\\mathbb{R}^{1+3}$. The equation arises naturally when considering the Yang-Mills-Higgs equations with Mexican hat type potentials. Our proof exploits the microlocal analysis of nonlinear wave interactions, but instead of employing information contained in the geometry of the wave front sets as in previous literatu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.05711","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"}