{"paper":{"title":"A new method for solving completely integrable PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Andrey Melnikov","submitted_at":"2012-12-08T01:13:35Z","abstract_excerpt":"The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS) equations, Kadomtzev-Petviashvili and many more completely integrable PDEs of mathematical physics are solved, using Zacharv-Shabath scheme. This last approach includes the use of a Lax pair, and has an advantage to be applied to wider class of equations, like difference equations, but has a disadvantage to be used only for \"rapidly decreasing solutions\". This t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1748","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"}