{"paper":{"title":"Ground States of a Nonlinear Curl-Curl Problem in Cylindrically Symmetric Media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Michael Plum, Thomas Bartsch, Tom\\'a\\v{s} Dohnal, Wolfgang Reichel","submitted_at":"2014-11-26T09:49:38Z","abstract_excerpt":"We consider the nonlinear curl-curl problem $\\nabla\\times\\nabla\\times U + V(x) U= \\Gamma(x)|U|^{p-1}U$ in $\\mathbb{R}^3$ related to the nonlinear Maxwell equations for monochromatic fields. We search for solutions as minimizers (ground states) of the corresponding energy functional defined on subspaces (defocusing case) or natural constraints (focusing case) of $H(\\mathrm{curl};\\mathbb{R}^3)$. Under a cylindrical symmetry assumption on the functions $V$ and $\\Gamma$ the variational problem can be posed in a symmetric subspace of $H(\\mathrm{curl};\\mathbb{R}^3)$. For a strongly defocusing case $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.7153","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"}