{"paper":{"title":"The Nonlinear Schr\\\"{o}dinger Equation in the Finite Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.comp-ph"],"primary_cat":"nlin.PS","authors_text":"Francisco R. Villatoro, Juan I. Ramos","submitted_at":"2013-01-17T00:04:13Z","abstract_excerpt":"A numerical study of the nonlinear Schr\\\"odinger (NLS) equation subject to homogeneous Dirichlet, Neumann and Robin boundary conditions in the finite line is presented. The results are compared with both the exact analytical ones for the initial-value problem (IVP) of the NLS equation and the numerical ones for periodic boundary conditions. It is shown that initial solutions obtained by truncating the exact N-soliton solution of the IVP of the NLS equation into a finite interval develop solitary waves that behave as solitons, even after collisions with the boundaries. For periodic and homogene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3951","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"}