{"paper":{"title":"Initial boundary value problem for the focusing NLS equation with Robin boundary condition: half-line approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"nlin.SI","authors_text":"Alexander Its, Dmitry Shepelsky","submitted_at":"2012-01-28T11:57:20Z","abstract_excerpt":"We consider the initial boundary value problem for the focusing nonlinear Schr\\\"odinger equation in the quarter plane $x>0,t>0$ in the case of decaying initial data (for $t=0$, as $x\\to +\\infty$) and the Robin boundary condition at $x=0$. We revisit the approach based on the simultaneous spectral analysis of the Lax pair equations [Fokas, 2002; Fokas, Its, Sung, 2005] and show that the approach can be implemented without any a priori assumptions on the long-time behavior of the boundary values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5948","kind":"arxiv","version":2},"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"}