{"paper":{"title":"Branch cuts of Stokes wave on deep water. Part II: Structure and location of branch points in infinite set of sheets of Riemann surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Pavel M. Lushnikov","submitted_at":"2015-09-11T05:45:29Z","abstract_excerpt":"Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the real line with fluid domain mapped into the lower complex half-plane. There is one square root branch point per spatial period of Stokes located in the upper complex half-plane at the distance $v_c$ from the real axis. The increase of Stokes wave height results in approaching $v_c$ to zero with the limiting Stokes wave formation at $v_c=0.$ The limiting Stok"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03393","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"}