{"paper":{"title":"Multisoliton solutions of the vector nonlinear Schr\\\"odinger equation (Kulish-Sklyanin model) and the vector mKdV equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"nlin.SI","authors_text":"Takayuki Tsuchida","submitted_at":"2015-12-06T21:50:13Z","abstract_excerpt":"There exist two natural vector generalizations of the completely integrable nonlinear Schr\\\"odinger (NLS) equation in $1+1$ dimensions: the well-known Manakov model and the lesser-known Kulish-Sklyanin model. In this paper, we propose a binary Darboux (or Zakharov-Shabat dressing) transformation that can be directly applied to the Kulish-Sklyanin model. By deriving a simple closed expression for iterations of the binary Darboux transformation, we obtain an explicit formula for the $N$-soliton solution of the Kulish-Sklyanin model under vanishing boundary conditions. Because the third-order sym"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01840","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"}