{"paper":{"title":"Traveling surface wave propagation on shallow water with variable bathymetry and current","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The Laplace cascade method yields a general algorithm to locate parameters for reflectionless long surface waves in shallow channels with variable bathymetry and current.","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"Semyon Churilov","submitted_at":"2026-05-03T07:18:38Z","abstract_excerpt":"Energy transmission over long distances by waves is a key mechanism for many natural processes. This possibility arises when an inhomogeneous medium is arranged in such a manner that it enables a certain type of wave to propagate with virtually no reflection or scattering. By application of the Laplace cascade method for integrating second-order hyperbolic equations, a general algorithm for finding the parameters of inhomogeneous non-reflecting flows is proposed. The algorithm is applied to the problem of long linear surface waves propagation in a channel with variable cross-section. The gener"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By application of the Laplace cascade method for integrating second-order hyperbolic equations, a general algorithm for finding the parameters of inhomogeneous reflectionless flows is proposed. The algorithm is applied to the problem of long linear surface waves propagation in a channel with variable cross-section.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the physical setup (variable bathymetry, current, shallow water) can be arranged so the wave equation admits reflectionless traveling-wave solutions that the Laplace cascade method can systematically locate, without significant nonlinear or three-dimensional effects.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A general algorithm based on the Laplace cascade method identifies parameters of inhomogeneous reflectionless flows for long linear surface waves on shallow water with variable bathymetry.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Laplace cascade method yields a general algorithm to locate parameters for reflectionless long surface waves in shallow channels with variable bathymetry and current.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4dedabc345a62304854af147ce5d9771c136f403f16b6eca6a3a30c48cf3010b"},"source":{"id":"2605.01751","kind":"arxiv","version":2},"verdict":{"id":"ffb46e9c-15ba-4bb9-b4f7-33e029d71800","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T16:44:55.234353Z","strongest_claim":"By application of the Laplace cascade method for integrating second-order hyperbolic equations, a general algorithm for finding the parameters of inhomogeneous reflectionless flows is proposed. The algorithm is applied to the problem of long linear surface waves propagation in a channel with variable cross-section.","one_line_summary":"A general algorithm based on the Laplace cascade method identifies parameters of inhomogeneous reflectionless flows for long linear surface waves on shallow water with variable bathymetry.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the physical setup (variable bathymetry, current, shallow water) can be arranged so the wave equation admits reflectionless traveling-wave solutions that the Laplace cascade method can systematically locate, without significant nonlinear or three-dimensional effects.","pith_extraction_headline":"The Laplace cascade method yields a general algorithm to locate parameters for reflectionless long surface waves in shallow channels with variable bathymetry and current."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01751/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T17:37:09.312094Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T05:01:22.952782Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:00:32.057177Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ad4eb1d42e68c5b4b245dad920461b2cdf53c23b6264bb1438e908c9aa64404e"},"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"}