{"paper":{"title":"Unified Approach to KdV Modulations","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Alexander L.Krylov, Gennady A.El, Stephanos Venakides","submitted_at":"2000-08-04T18:24:45Z","abstract_excerpt":"We develop a unified approach to integrating the Whitham modulation equations. Our approach is based on the formulation of the initial value problem for the zero dispersion KdV as the steepest descent for the scalar Riemann-Hilbert problem, developed by Deift, Venakides, and Zhou, 1997, and on the method of generating differentials for the KdV-Whitham hierarchy proposed by El, 1996. By assuming the hyperbolicity of the zero-dispersion limit for the KdV with general initial data, we bypass the inverse scattering transform and produce the symmetric system of algebraic equations describing motion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0008007","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"}