{"id":"https://openalex.org/W2127580059","doi":"https://doi.org/10.1109/ecc.2015.7330526","title":"Lagrangian controllability of the Korteweg-de Vries equation with a higher order velocity field for the N-solitons solution","display_name":"Lagrangian controllability of the Korteweg-de Vries equation with a higher order velocity field for the N-solitons solution","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W2127580059","doi":"https://doi.org/10.1109/ecc.2015.7330526","mag":"2127580059"},"language":"en","primary_location":{"id":"doi:10.1109/ecc.2015.7330526","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2015.7330526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 European Control Conference (ECC)","raw_type":"proceedings-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/A5051831147","display_name":"Ludovick Gagnon","orcid":"https://orcid.org/0000-0002-8329-7983"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ludovick Gagnon","raw_affiliation_strings":["Sorbonnes Universites, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France","Sorbonnes Universit\u00e9s, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sorbonnes Universites, UMR 7598, Laboratoire Jacques-Louis Lions, Paris, France","institution_ids":["https://openalex.org/I4210158291"]},{"raw_affiliation_string":"Sorbonnes Universit\u00e9s, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5051831147"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09976905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"365","issue":null,"first_page":"61","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9998999834060669,"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":0.9998999834060669,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9983999729156494,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9936000108718872,"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":0.7519443035125732},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.7470324635505676},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.6042906045913696},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5701590776443481},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5447136163711548},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4719611406326294},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.41684624552726746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.27821409702301025},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2697022557258606},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22446590662002563},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17396512627601624}],"concepts":[{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.7519443035125732},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.7470324635505676},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.6042906045913696},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5701590776443481},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5447136163711548},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4719611406326294},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.41684624552726746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27821409702301025},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2697022557258606},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22446590662002563},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17396512627601624},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ecc.2015.7330526","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ecc.2015.7330526","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01475391v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01475391","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"European Control Conference, Jul 2015, Linz, Austria. &#x27E8;10.1109/ECC.2015.7330526&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W95194503","https://openalex.org/W305332711","https://openalex.org/W1427593441","https://openalex.org/W1986788497","https://openalex.org/W1989760690","https://openalex.org/W1993128651","https://openalex.org/W1995064792","https://openalex.org/W2027595215","https://openalex.org/W2049457404","https://openalex.org/W2057207324","https://openalex.org/W2082137733","https://openalex.org/W2086519672","https://openalex.org/W2094295163","https://openalex.org/W2501490850","https://openalex.org/W2585127113","https://openalex.org/W2950391361","https://openalex.org/W4300069495","https://openalex.org/W6733060347"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2411113819","https://openalex.org/W2072887367","https://openalex.org/W2332386680","https://openalex.org/W2561315646","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W2164760767","https://openalex.org/W4205698120","https://openalex.org/W2024710114"],"abstract_inverted_index":{"In":[0],"this":[1,84],"article,":[2],"we":[3],"study":[4],"the":[5,9,15,21,35,71,87],"Lagrangian":[6],"controllablity":[7],"of":[8,34,83,89,92],"Korteweg-de":[10],"Vries":[11],"(KdV)":[12],"equation":[13],"with":[14],"higher":[16],"order":[17],"velocity":[18],"field":[19],"for":[20,30,66],"N-solitons":[22],"solution":[23],"given":[24,32],"in":[25,74],"[4].":[26],"We":[27],"prove":[28],"that,":[29],"a":[31,63],"depth":[33],"fluid":[36,72],"h":[37],"<sub":[38,45,56],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[39,46,57],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">0</sub>":[40],",":[41,59],"there":[42,61],"exists":[43,62],"L":[44,53,55],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">N</sub>":[47,58],">":[48,79],"0":[49],"such":[50],"that":[51],"if":[52],"<;":[54],"then":[60],"time":[64],"T":[65],"which":[67],"one":[68],"can":[69],"transport":[70],"located":[73],"[0,":[75],"L]":[76],"to":[77],"x":[78],"L.":[80],"Physical":[81],"applications":[82],"result":[85],"include":[86],"transportation":[88],"sediment":[90],"and":[91],"polluted":[93],"water.":[94]},"counts_by_year":[],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
