{"id":"https://openalex.org/W4226306521","doi":"https://doi.org/10.1137/21m1458387","title":"Around Plane Waves Solutions of the Schr\u00f6dinger--Langevin Equation","display_name":"Around Plane Waves Solutions of the Schr\u00f6dinger--Langevin Equation","publication_year":2022,"publication_date":"2022-09-06","ids":{"openalex":"https://openalex.org/W4226306521","doi":"https://doi.org/10.1137/21m1458387"},"language":"en","primary_location":{"id":"doi:10.1137/21m1458387","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1458387","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-03409804","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024448103","display_name":"Quentin Chauleur","orcid":"https://orcid.org/0000-0002-8771-094X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Quentin Chauleur","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5045956945","display_name":"Erwan Faou","orcid":"https://orcid.org/0000-0001-8939-0014"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Erwan Faou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12034896,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"5","first_page":"5103","last_page":"5125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9952999949455261,"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":0.9952999949455261,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9668999910354614,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9532999992370605,"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/sobolev-space","display_name":"Sobolev space","score":0.7695050835609436},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.604109525680542},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6011413335800171},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5209997296333313},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.5186557173728943},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5121514797210693},{"id":"https://openalex.org/keywords/plane-wave","display_name":"Plane wave","score":0.5067995190620422},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4925175607204437},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4812473952770233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46418920159339905},{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.4550952613353729},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.4512466788291931},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.42763036489486694},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3604661822319031},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.29588478803634644},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1479790210723877},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10983625054359436}],"concepts":[{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7695050835609436},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.604109525680542},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6011413335800171},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5209997296333313},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.5186557173728943},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5121514797210693},{"id":"https://openalex.org/C40308292","wikidata":"https://www.wikidata.org/wiki/Q122518","display_name":"Plane wave","level":2,"score":0.5067995190620422},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4925175607204437},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4812473952770233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46418920159339905},{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.4550952613353729},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.4512466788291931},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.42763036489486694},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3604661822319031},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.29588478803634644},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1479790210723877},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10983625054359436}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m1458387","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1458387","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:HAL:hal-03409804v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03409804","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":"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, 2022, 54 (5), pp.5103-5125. ⟨10.1137/21M1458387⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2111.01487","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2111.01487","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03409804v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03409804","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":"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, 2022, 54 (5), pp.5103-5125. ⟨10.1137/21M1458387⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3597637701","display_name":"Centre de Math\u00e9matiques Henri Lebesgue : fondements, interactions, applications et Formation","funder_award_id":"ANR-11-LABX-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1859791165","https://openalex.org/W1977120242","https://openalex.org/W1978219042","https://openalex.org/W1984948191","https://openalex.org/W1988599722","https://openalex.org/W1993142553","https://openalex.org/W1996164347","https://openalex.org/W1996943823","https://openalex.org/W2006638341","https://openalex.org/W2020107848","https://openalex.org/W2071357402","https://openalex.org/W2076523251","https://openalex.org/W2080454515","https://openalex.org/W2086524222","https://openalex.org/W2088629022","https://openalex.org/W2171594451","https://openalex.org/W2563583896","https://openalex.org/W2581152228","https://openalex.org/W2606215050","https://openalex.org/W2661764014","https://openalex.org/W2795033786","https://openalex.org/W2902944228","https://openalex.org/W2946420937","https://openalex.org/W2964320191","https://openalex.org/W2964326332","https://openalex.org/W2971652502","https://openalex.org/W2980337949","https://openalex.org/W3086610488","https://openalex.org/W3135202607","https://openalex.org/W3159388761"],"related_works":["https://openalex.org/W16907912","https://openalex.org/W21181848","https://openalex.org/W24180715","https://openalex.org/W12664150","https://openalex.org/W31981613","https://openalex.org/W20998167","https://openalex.org/W6419794","https://openalex.org/W9994322","https://openalex.org/W6256144","https://openalex.org/W13263030"],"abstract_inverted_index":{"We":[0,26,74],"consider":[1],"the":[2,10,38,50,66],"logarithmic":[3],"Schr\u00f6dinger":[4],"equations":[5],"with":[6],"damping,":[7,41],"also":[8,75],"called":[9],"Schr\u00f6dinger--Langevin":[11],"equation.":[12],"On":[13],"a":[14,71],"periodic":[15],"domain,":[16],"this":[17],"equation":[18],"possesses":[19],"plane":[20,72],"wave":[21],"solutions":[22,30,54],"that":[23,28,44],"are":[24,31,55],"explicit.":[25],"prove":[27,43],"these":[29,53],"asymptotically":[32],"stable":[33,56],"in":[34,57],"Sobolev":[35,59],"regularity.":[36],"In":[37],"case":[39],"without":[40],"we":[42],"for":[45,61],"almost":[46],"all":[47],"values":[48],"of":[49],"nonlinear":[51],"parameter,":[52],"high":[58],"regularity":[60],"arbitrary":[62],"long":[63],"times":[64],"when":[65],"solution":[67],"is":[68],"close":[69],"to":[70],"wave.":[73],"show":[76],"and":[77],"discuss":[78],"numerical":[79],"experiments":[80],"illustrating":[81],"our":[82],"results.":[83]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2022-05-05T00:00:00"}