{"paper":{"title":"One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"physics.optics","authors_text":"Boris A. Malomed, Vitaly Lutsky","submitted_at":"2015-01-30T14:16:30Z","abstract_excerpt":"We introduce a model of one- and two-dimensional (1D and 2D) optical media with the $\\chi ^{(2)}$ nonlinearity whose local strength is subject to cusp-shaped spatial modulation, $\\chi ^{(2)}\\sim r^{-\\alpha }$, with $\\alpha >0$, which can be induced by spatially nonuniform poling. Using analytical and numerical methods, we demonstrate that this setting supports 1D and 2D fundamental solitons, at $\\alpha <1$ and $\\alpha <2$, respectively. The 1D solitons have a small instability region, while the 2D solitons have a stability region at $\\alpha <0.5$ and are unstable at $\\alpha >0.5$. 2D solitary "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07782","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"}