{"paper":{"title":"Traveling-wave solutions and structure-preserving numerical methods for a hyperbolic approximation of the Korteweg-de Vries equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Abhijit Biswas, David I. Ketcheson, Hendrik Ranocha, Jochen Sch\\\"utz","submitted_at":"2024-12-22T18:14:24Z","abstract_excerpt":"We study the recently-proposed hyperbolic approximation of the Korteweg-de Vries equation (KdV). We show that this approximation, which we call KdVH, possesses a rich variety of solutions, including solitary wave solutions that approximate KdV solitons, as well as other solitary and periodic solutions that are related to higher-order water wave models, and may include singularities. We analyze a class of implicit-explicit Runge-Kutta time discretizations for KdVH that are asymptotic preserving, energy conserving, and can be applied to other hyperbolized systems. We also develop structure-prese"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.17117","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.17117/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}