{"paper":{"title":"Analytical and numerical studying of the perturbed Korteweg--de Vries equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Dmitry I. Sinelshchikov, Nikolay A. Kudryashov","submitted_at":"2014-09-23T19:19:50Z","abstract_excerpt":"The perturbed Korteweg--de Vries equation is considered. This equation is used for the description of one--dimensional viscous gas dynamics, nonlinear waves in a liquid with gas bubbles and nonlinear acoustic waves. The integrability of this equation is investigated using the Painlev\\'e approach. The condition for parameters for the integrability of the perturbed Korteweg--de Vries equation equation is established. New classical and nonclassical symmetries admitted by this equation are found. All corresponding symmetry reductions are obtained. New exact solutions of these reductions are constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.6703","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"}