{"paper":{"title":"Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Boris A. Malomed, Hidetsugu Sakaguchi","submitted_at":"2012-02-06T06:02:36Z","abstract_excerpt":"We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional (2D) geometry, in the form of a circle with contrast $\\Delta g$ of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation (VA) and Vakhitov-Kolokolov (VK) stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton's norm scales as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.1052","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"}