{"paper":{"title":"Group-invariant solutions of semilinear Schrodinger equations in multi- dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Stephen C. Anco, Wei Feng","submitted_at":"2013-01-23T15:13:29Z","abstract_excerpt":"Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schrodinger equations in dimensions $n\\neq 1$. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the conformal power $p=4/n$ relevant for critical dynamics.The methods involve, firstly, reduction of the semilinear Schrodinger equations to group-invariant complex 2nd order ODEs with respect to an optimal set of one-dimensional point symmetry groups, and secondly, use of inherited symmetries, hidden symmetries, and conditional "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5529","kind":"arxiv","version":5},"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"}