{"id":"https://openalex.org/W2980332465","doi":"https://doi.org/10.1137/18m1231638","title":"On the Existence and Instability of Solitary Water Waves with a Finite Dipole","display_name":"On the Existence and Instability of Solitary Water Waves with a Finite Dipole","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2980332465","doi":"https://doi.org/10.1137/18m1231638","mag":"2980332465"},"language":"en","primary_location":{"id":"doi:10.1137/18m1231638","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1231638","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5091538572","display_name":"Hung Le","orcid":"https://orcid.org/0000-0003-3616-8588"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hung Le","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091538572"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1418,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76697602,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"51","issue":"5","first_page":"4074","last_page":"4104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.779579758644104},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.6405251622200012},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.56717848777771},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.48950254917144775},{"id":"https://openalex.org/keywords/potential-vorticity","display_name":"Potential vorticity","score":0.48358815908432007},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4544144868850708},{"id":"https://openalex.org/keywords/surface-tension","display_name":"Surface tension","score":0.4492571949958801},{"id":"https://openalex.org/keywords/free-surface","display_name":"Free surface","score":0.4369840621948242},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43157997727394104},{"id":"https://openalex.org/keywords/dipole","display_name":"Dipole","score":0.4145168960094452},{"id":"https://openalex.org/keywords/implicit-function-theorem","display_name":"Implicit function theorem","score":0.4139367938041687},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.32850000262260437},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.24756386876106262},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22384309768676758},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.149217426776886},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09043100476264954}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.779579758644104},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.6405251622200012},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.56717848777771},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.48950254917144775},{"id":"https://openalex.org/C157331469","wikidata":"https://www.wikidata.org/wiki/Q1418563","display_name":"Potential vorticity","level":4,"score":0.48358815908432007},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4544144868850708},{"id":"https://openalex.org/C8892853","wikidata":"https://www.wikidata.org/wiki/Q170749","display_name":"Surface tension","level":2,"score":0.4492571949958801},{"id":"https://openalex.org/C171889981","wikidata":"https://www.wikidata.org/wiki/Q1454008","display_name":"Free surface","level":2,"score":0.4369840621948242},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43157997727394104},{"id":"https://openalex.org/C173523689","wikidata":"https://www.wikidata.org/wiki/Q215589","display_name":"Dipole","level":2,"score":0.4145168960094452},{"id":"https://openalex.org/C138578839","wikidata":"https://www.wikidata.org/wiki/Q848375","display_name":"Implicit function theorem","level":2,"score":0.4139367938041687},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.32850000262260437},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24756386876106262},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22384309768676758},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.149217426776886},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09043100476264954},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1231638","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1231638","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation","score":0.5899999737739563}],"awards":[{"id":"https://openalex.org/G267907848","display_name":null,"funder_award_id":"15499","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6772013485","display_name":"Research in Applied Dynamical Systems","funder_award_id":"1710989","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7296782440","display_name":null,"funder_award_id":"DMS-171098","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7586248288","display_name":"KUMU Conference on PDE, Dynamical Systems, and Applications","funder_award_id":"1549934","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7601687993","display_name":null,"funder_award_id":"DMS-1549934","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8646746994","display_name":null,"funder_award_id":"DMS-1710989","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1972412915","https://openalex.org/W1973955700","https://openalex.org/W1976496016","https://openalex.org/W2003405066","https://openalex.org/W2005293388","https://openalex.org/W2006365463","https://openalex.org/W2011000117","https://openalex.org/W2032625117","https://openalex.org/W2033946502","https://openalex.org/W2038213678","https://openalex.org/W2043168291","https://openalex.org/W2059552911","https://openalex.org/W2071757261","https://openalex.org/W2090885565","https://openalex.org/W2101731201","https://openalex.org/W2141854720","https://openalex.org/W2143303188","https://openalex.org/W2154251648","https://openalex.org/W2167156195","https://openalex.org/W2294207300","https://openalex.org/W2592381638","https://openalex.org/W2891940291","https://openalex.org/W3101461424","https://openalex.org/W3102949457","https://openalex.org/W3104178066","https://openalex.org/W4213132260"],"related_works":["https://openalex.org/W80460452","https://openalex.org/W4225752357","https://openalex.org/W3098621800","https://openalex.org/W2005500739","https://openalex.org/W2087126627","https://openalex.org/W1989681580","https://openalex.org/W4366595827","https://openalex.org/W2168465040","https://openalex.org/W2021261631","https://openalex.org/W2039034912"],"abstract_inverted_index":{"This":[0,109],"paper":[1],"considers":[2],"the":[3,23,29,41,48,57,60,64,116],"existence":[4],"and":[5,27,124],"stability":[6],"properties":[7],"of":[8,17,59,69,83,96,115],"two-dimensional":[9],"solitary":[10,84],"waves":[11,30,85],"traversing":[12],"an":[13,74],"infinitely":[14],"deep":[15],"body":[16],"water.":[18],"We":[19],"assume":[20],"that":[21,28,62,90,102],"above":[22],"water":[24],"is":[25,52,66,91,101,105,110],"air":[26],"are":[31],"acted":[32],"upon":[33],"by":[34,121],"gravity":[35],"with":[36],"surface":[37],"tension":[38],"effects":[39],"on":[40],"air-water":[42],"interface.":[43],"In":[44],"particular,":[45],"we":[46,79],"study":[47],"case":[49],"where":[50],"there":[51],"a":[53,67,81,94,113],"finite":[54],"dipole":[55],"in":[56,93],"bulk":[58],"fluid,":[61],"is,":[63],"vorticity":[65],"sum":[68],"two":[70],"weighted":[71],"$\\delta$-functions.":[72],"Using":[73],"implicit":[75],"function":[76],"theorem":[77],"argument,":[78],"construct":[80],"family":[82,104],"solutions":[86],"for":[87],"this":[88,103],"system":[89],"exhaustive":[92],"neighborhood":[95],"$0$.":[97],"Our":[98],"main":[99],"result":[100],"conditionally":[106],"orbitally":[107],"unstable.":[108],"proved":[111],"using":[112],"modification":[114],"Grillakis--Shatah--Strauss":[117],"method":[118],"recently":[119],"introduced":[120],"Varholm,":[122],"Wahl\u00e9n,":[123],"Walsh.":[125]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}