{"paper":{"title":"A 2D Schrodinger equation with time-oscillating exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub","submitted_at":"2018-12-14T16:20:41Z","abstract_excerpt":"This paper deals with the 2-D Schr\\\"odinger equation with time-oscillating exponential nonlinearity $i\\partial_t u+\\Delta u= \\theta(\\omega t)\\big(e^{4\\pi|u|^2}-1\\big)$, where $\\theta$ is a periodic $C^1$-function. We prove that for a class of initial data $u_0 \\in H^1(\\mathbb{R}^2)$, the solution $u_{\\omega}$ converges, as $|\\omega|$ tends to infinity to the solution $U$ of the limiting equation $i\\partial_t U+\\Delta U= I(\\theta)\\big(e^{4\\pi|U|^2}-1\\big)$ with the same initial data, where $I(\\theta)$ is the average of $\\theta$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.06005","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"}