{"paper":{"title":"Finite-gap solutions of the Sine-Gordon equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"V.P.Kotlarov","submitted_at":"2014-01-17T17:37:46Z","abstract_excerpt":"This paper contains first results on the finite-gap integration of the Sine-Gordon equation. They were published on Russian in 1976. The papers \\cite{Koz}, \\cite{KK}, \\cite{KK02} have been rewritten in the English language with small modifications for a convenience. Such a translation was made due to requests of some interested readers.\n  In those papers, the method of constructing of the finite-gap solutions of the equation $u_{tt}-u_{xx}+\\sin u=0$ was proposed. The explicit formulae were obtained for these solutions. The formulae are constructed in terms of $\\theta$-functions and they are an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4410","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"}