{"id":"https://openalex.org/W2014165617","doi":"https://doi.org/10.1137/s0036139997317853","title":"High-Frequency Asymptotics of Edge Waves on a Beach of Nonconstant Slope","display_name":"High-Frequency Asymptotics of Edge Waves on a Beach of Nonconstant Slope","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2014165617","doi":"https://doi.org/10.1137/s0036139997317853","mag":"2014165617"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139997317853","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997317853","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091879210","display_name":"Anatoli Merzon","orcid":"https://orcid.org/0000-0002-2916-9884"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. E. Merzon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5044033525","display_name":"P. Zhevandrov","orcid":"https://orcid.org/0000-0001-8020-9688"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. N. Zhevandrov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5091879210"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5253,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.81951814,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"59","issue":"2","first_page":"529","last_page":"546"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.701266348361969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6958999633789062},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6319692134857178},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.5141913890838623},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5065373182296753},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4726516306400299},{"id":"https://openalex.org/keywords/cylinder","display_name":"Cylinder","score":0.45072460174560547},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.43977367877960205}],"concepts":[{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.701266348361969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6958999633789062},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6319692134857178},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5141913890838623},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5065373182296753},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4726516306400299},{"id":"https://openalex.org/C203311528","wikidata":"https://www.wikidata.org/wiki/Q34132","display_name":"Cylinder","level":2,"score":0.45072460174560547},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.43977367877960205}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139997317853","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139997317853","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:tubiblio.ulb.tu-darmstadt.de:7445","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/Merzon=3AAnatol_E=2E=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1548520532","https://openalex.org/W1978912560","https://openalex.org/W2030419859","https://openalex.org/W2043145045","https://openalex.org/W2046122206","https://openalex.org/W2051437422","https://openalex.org/W2064772542","https://openalex.org/W2149096508","https://openalex.org/W2156353553","https://openalex.org/W2160743531","https://openalex.org/W2496940745","https://openalex.org/W2943046378","https://openalex.org/W3042341830"],"related_works":["https://openalex.org/W2306553012","https://openalex.org/W4251417359","https://openalex.org/W4229993731","https://openalex.org/W2381059884","https://openalex.org/W2372756075","https://openalex.org/W1979193983","https://openalex.org/W2098894475","https://openalex.org/W2053857640","https://openalex.org/W2133690079","https://openalex.org/W2111215486"],"abstract_inverted_index":{"The":[0,30,96],"paper":[1],"is":[2,107],"devoted":[3],"to":[4,28,68,76],"the":[5,23,64,69,102,105,118],"construction":[6,103],"of":[7,12,19,32,61,72,88,91,104,111],"asymptotic":[8,38],"expansions":[9],"for":[10,101,117],"frequencies":[11],"water":[13],"waves":[14],"trapped":[15,80],"by":[16,81,86],"a":[17,59,89,112],"beach":[18,60],"nonconstant":[20],"slope":[21,63],"as":[22],"longshore":[24],"wave":[25],"number":[26],"tends":[27],"infinity.":[29],"existence":[31],"such":[33],"trapping":[34],"modes":[35],"in":[36,43,121],"this":[37],"regime":[39],"was":[40],"proved":[41],"recently":[42],"[A.-S.":[44],"Bonnet-Ben":[45],"Dhia":[46],"and":[47,85],"P.":[48],"Joly,":[49],"SIAM":[50],"J.":[51],"Appl.":[52],"Math.,":[53],"53":[54],"(1993),":[55],"pp.":[56],"1507--1550].":[57],"For":[58],"constant":[62],"formulas":[65],"obtained":[66],"reduce":[67],"classical":[70],"result":[71],"Ursell.":[73],"Some":[74],"generalizations":[75],"other":[77],"geometries":[78],"(waves":[79],"afloating":[82],"semisubmerged":[83],"cylinder":[84],"shores":[87],"channel":[90],"finite":[92],"width)":[93],"are":[94],"indicated.":[95],"main":[97],"analytical":[98],"tool":[99],"used":[100],"asymptotics":[106],"an":[108,122],"explicit":[109],"solution":[110],"mixed":[113],"boundary":[114,126],"value":[115],"problem":[116],"Helmholtz":[119],"equation":[120],"angle":[123],"with":[124],"nonhomogeneous":[125],"conditions.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
