{"id":"https://openalex.org/W2076997135","doi":"https://doi.org/10.1137/090779103","title":"Solitonic Asymptotics for the Korteweg\u2013de Vries Equation in the Small Dispersion Limit","display_name":"Solitonic Asymptotics for the Korteweg\u2013de Vries Equation in the Small Dispersion Limit","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2076997135","doi":"https://doi.org/10.1137/090779103","mag":"2076997135"},"language":"en","primary_location":{"id":"doi:10.1137/090779103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090779103","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2078.1/73376","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051237961","display_name":"Tom Claeys","orcid":"https://orcid.org/0000-0001-9622-2668"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tom Claeys","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050659081","display_name":"\u0422\u0430\u043c\u0430\u0440\u0430 \u0413\u0440\u0430\u0432\u0430","orcid":"https://orcid.org/0000-0001-7640-7331"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tamara Grava","raw_affiliation_strings":["School of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7718,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.91457107,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"42","issue":"5","first_page":"2132","last_page":"2154"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9991999864578247,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.956379234790802},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6822942495346069},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6809382438659668},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.6580018997192383},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6059851050376892},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.5713334083557129},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.5670192241668701},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5424445867538452},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5101197361946106},{"id":"https://openalex.org/keywords/trailing-edge","display_name":"Trailing edge","score":0.4845234751701355},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.46504345536231995},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2871185541152954},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.13058072328567505},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11336159706115723},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10808947682380676}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.956379234790802},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6822942495346069},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6809382438659668},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.6580018997192383},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6059851050376892},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.5713334083557129},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5670192241668701},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5424445867538452},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5101197361946106},{"id":"https://openalex.org/C28317120","wikidata":"https://www.wikidata.org/wiki/Q975211","display_name":"Trailing edge","level":2,"score":0.4845234751701355},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.46504345536231995},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2871185541152954},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.13058072328567505},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11336159706115723},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10808947682380676},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090779103","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090779103","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"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/3b9f0190-a69f-4dbe-acb5-b15c7f9ec4c4","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/3b9f0190-a69f-4dbe-acb5-b15c7f9ec4c4","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Claeys, T & Grava, T 2010, 'Solitonic Asymptotics for the Korteweg\u2013de Vries Equation in the Small Dispersion Limit', SIAM Journal on Mathematical Analysis, vol. 42, no. 5, pp. 2132-2154. https://doi.org/10.1137/090779103","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dial.uclouvain.be:boreal:73376","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/73376","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, Vol. 42, no. 5, p. 2132-2154 (2010)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dial.uclouvain.be:boreal:73376","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/73376","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, Vol. 42, no. 5, p. 2132-2154 (2010)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W68023263","https://openalex.org/W1520582556","https://openalex.org/W1544715525","https://openalex.org/W1562723252","https://openalex.org/W1590857171","https://openalex.org/W1964062536","https://openalex.org/W1966188617","https://openalex.org/W1981257234","https://openalex.org/W1986788497","https://openalex.org/W1993986705","https://openalex.org/W1998313731","https://openalex.org/W2012657368","https://openalex.org/W2016002683","https://openalex.org/W2016393303","https://openalex.org/W2031464598","https://openalex.org/W2039188392","https://openalex.org/W2061491621","https://openalex.org/W2062565740","https://openalex.org/W2082978869","https://openalex.org/W2101309150","https://openalex.org/W2103704379","https://openalex.org/W2137247574","https://openalex.org/W2139145457","https://openalex.org/W2296142190","https://openalex.org/W3098871862","https://openalex.org/W3099611575","https://openalex.org/W4237362312","https://openalex.org/W4239163694","https://openalex.org/W4249126432"],"related_works":["https://openalex.org/W1985080983","https://openalex.org/W2102153656","https://openalex.org/W1971248990","https://openalex.org/W2774129652","https://openalex.org/W2058757124","https://openalex.org/W2263050974","https://openalex.org/W2353815637","https://openalex.org/W2067598262","https://openalex.org/W2223488821","https://openalex.org/W2012493829"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,7,27,31,34,41,50,61,68,78],"small":[3],"dispersion":[4],"limit":[5],"for":[6,49],"Korteweg-de":[8],"Vries":[9],"(KdV)":[10],"equation":[11],"u(t)":[12],"+":[13,15],"6uu(x)":[14],"epsilon(2)u(xxx)":[16],"=":[17],"0":[18],"in":[19,53],"a":[20,54],"critical":[21],"scaling":[22,56],"regime":[23],"where":[24,33],"x":[25],"approaches":[26],"trailing":[28,69],"edge":[29],"of":[30,77],"region":[32],"KdV":[35,51,79],"solution":[36,52],"shows":[37,59],"oscillatory":[38],"behavior.":[39],"Using":[40],"Riemann-Hilbert":[42],"approach,":[43],"we":[44],"obtain":[45],"an":[46],"asymptotic":[47],"expansion":[48],"double":[55],"limit,":[57],"which":[58],"that":[60],"oscillations":[62],"degenerate":[63],"to":[64],"sharp":[65],"pulses":[66,73],"near":[67],"edge.":[70],"Locally":[71],"those":[72],"resemble":[74],"soliton":[75],"solutions":[76],"equation.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}