{"paper":{"title":"Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Non-Linear Schr\\\"{o}dinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"A. H. Vartanian","submitted_at":"2002-10-22T02:59:08Z","abstract_excerpt":"For Lax-pair isospectral deformations whose associated spectrum, for given initial data, consists of the disjoint union of a finitely denumerable discrete spectrum (solitons) and a continuous spectrum (continuum), the matrix Riemann-Hilbert problem approach is used to derive the leading-order asymptotics as $| t | \\to \\infty$ $(x/t \\sim \\mathcal{O} (1))$ of solutions $(u = u(x,t))$ to the Cauchy problem for the defocusing non-linear Schr\\\"{o}dinger equation (D${}_{f}$NLSE), $\\mi \\partial_{t}u + \\partial_{x}^{2}u - 2(| u |^{2} - 1) u = 0$, with finite-density initial data $u(x,0) =_{x \\to \\pm \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0210050","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"}