{"paper":{"title":"Nonlinear Schr\\\"odinger equation on the half-line with nonlinear boundary condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ahmet Batal, T\\\"urker \\\"Ozsar{\\i}","submitted_at":"2015-07-16T17:40:24Z","abstract_excerpt":"In this paper, we study the initial boundary value problem for nonlinear Schr\\\"odinger equations on the half-line with nonlinear boundary conditions of type $u_x(0,t)+\\lambda|u(0,t)|^ru(0,t)=0,$ $\\lambda\\in\\mathbb{R}-\\{0\\}$, $r> 0$. We discuss the local well-posedness when the initial data $u_0=u(x,0)$ belongs to an $L^2$-based inhomogeneous Sobolev space $H^s(\\mathbb{R}_+)$ with $s\\in \\left(\\frac{1}{2},\\frac{7}{2}\\right)-\\{\\frac{3}{2}\\}$. We deal with the nonlinear boundary condition by first studying the linear Schr\\\"odinger equation with a time-dependent inhomogeneous Neumann boundary condi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04666","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"}