{"paper":{"title":"Scattering in the weighted $L^2$-space for a 2D nonlinear Schr\\\"odinger equation with inhomogeneous exponential nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Abdelwahab Bensouilah, Mohamed Majdoub, Van Duong Dinh","submitted_at":"2018-10-21T15:24:18Z","abstract_excerpt":"We investigate the defocusing inhomogeneous nonlinear Schr\\\"odinger equation\n  $$ i \\partial_tu + \\Delta u = |x|^{-b} \\left({\\rm e}^{\\alpha|u|^2} - 1- \\alpha |u|^2 \\right) u, \\quad u(0)=u_0, \\quad x \\in \\mathbb{R}^2,\n  $$ with $0<b<1$ and $\\alpha=2\\pi(2-b)$. First we show the decay of global solutions by assuming that the initial data $u_0$ belongs to the weighted space $\\Sigma(\\mathbb{R}^2)=\\{\\,u\\in H^1(\\mathbb{R}^2) \\ : \\ |x|u\\in L^2(\\mathbb{R}^2)\\,\\}$. Then we combine the local theory with the decay estimate to obtain scattering in $\\Sigma$ when the Hamiltonian is below the value $\\frac{2}{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08974","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"}