{"paper":{"title":"The Non-Linear Schr\\\"odinger Equation with a periodic {\\bf{$\\delta$}}--interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Gustavo Ponce, Jaime Angulo","submitted_at":"2011-01-18T23:31:03Z","abstract_excerpt":"We study the existence and stability of the standing waves for the periodic cubic nonlinear Schr\\\"odinger equation with a point defect determined by a periodic Dirac distribution at the origin. This equation admits a smooth curve of positive periodic solutions in the form of standing waves with a profile given by the Jacobi elliptic function of dnoidal type. Via a perturbation method and continuation argument, we obtain that in the case of an attractive defect the standing wave solutions are stable in $H^1_{per}$ with respect to perturbations which have the same period as the wave itself. In t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3582","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"}