{"paper":{"title":"Extended KdV equation for the case of uneven bottom","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Anna Karczewska, Piotr Rozmej","submitted_at":"2018-10-16T17:38:38Z","abstract_excerpt":"We derived consistently, according to the second order perturbation approach, the extended KdV equation for an uneven bottom for the case of $\\alpha=O(\\beta)$ and $\\delta=O(\\beta^2)$. This equation can be obtained only when the bottom is given by a piecewise linear function. For the case of $\\alpha=O(\\beta)$ and $\\delta=O(\\beta)$, a unidirectional wave equation is derived in the first order approach with the same limitation for the bottom profile."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07183","kind":"arxiv","version":3},"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"}