{"id":"https://openalex.org/W2011846139","doi":"https://doi.org/10.1007/s00332-014-9193-x","title":"Stochastic Nonlinear Schr\u00f6dinger Equations with Linear Multiplicative Noise: Rescaling Approach","display_name":"Stochastic Nonlinear Schr\u00f6dinger Equations with Linear Multiplicative Noise: Rescaling Approach","publication_year":2014,"publication_date":"2014-02-25","ids":{"openalex":"https://openalex.org/W2011846139","doi":"https://doi.org/10.1007/s00332-014-9193-x","mag":"2011846139"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-014-9193-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-014-9193-x","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","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/A5102862771","display_name":"Viorel Barbu","orcid":"https://orcid.org/0000-0002-4715-9778"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Viorel Barbu","raw_affiliation_strings":["Al.I. Cuza University, 700506 , Iasi, Romania","Octav Mayer Institute of Mathematics, Romanian Academy, 700506 , Iasi, Romania","Romanian Academy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Al.I. Cuza University, 700506 , Iasi, Romania","institution_ids":["https://openalex.org/I138164181"]},{"raw_affiliation_string":"Octav Mayer Institute of Mathematics, Romanian Academy, 700506 , Iasi, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Romanian Academy","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010020158","display_name":"Michael R\u00f6ckner","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Michael R\u00f6ckner","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, 33501 , Bielefeld, Germany","Universit\u00e4t Bielefeld"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, 33501 , Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]},{"raw_affiliation_string":"Universit\u00e4t Bielefeld","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100617479","display_name":"Deng Zhang","orcid":"https://orcid.org/0000-0001-8080-2860"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Deng Zhang","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, 33501 , Bielefeld, Germany","Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","Chinese Academy of Sciences","Universit\u00e4t Bielefeld"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Bielefeld, 33501 , Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]},{"raw_affiliation_string":"Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Universit\u00e4t Bielefeld","institution_ids":["https://openalex.org/I20121455"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5102862771"],"corresponding_institution_ids":["https://openalex.org/I138164181","https://openalex.org/I58077936"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.4805,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.94303744,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"24","issue":"3","first_page":"383","last_page":"409"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9991000294685364,"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":0.9991000294685364,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.825093150138855},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6572529673576355},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.6146734356880188},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5421356558799744},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5147950053215027},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.48907309770584106},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4759768545627594},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4489056468009949},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.42803120613098145},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.41902655363082886},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4148518443107605},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.412425696849823},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4107816815376282},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16422158479690552},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10648214817047119},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09588590264320374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.825093150138855},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6572529673576355},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.6146734356880188},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5421356558799744},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5147950053215027},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.48907309770584106},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4759768545627594},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4489056468009949},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.42803120613098145},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.41902655363082886},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4148518443107605},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.412425696849823},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4107816815376282},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16422158479690552},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10648214817047119},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09588590264320374},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C131021393","wikidata":"https://www.wikidata.org/wiki/Q7512759","display_name":"Signal transfer function","level":4,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C13412647","wikidata":"https://www.wikidata.org/wiki/Q174948","display_name":"Analog signal","level":3,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00332-014-9193-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-014-9193-x","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:pub.uni-bielefeld.de:2685876","is_oa":false,"landing_page_url":"https://pub.uni-bielefeld.de/record/2685876","pdf_url":null,"source":{"id":"https://openalex.org/S4306401624","display_name":"Publikationen an der Universit\u00e4t Bielefeld (Universit\u00e4t Bielefeld)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Barbu V, R\u00f6ckner M, Zhang D. Stochastic Nonlinear Schr\u00f6dinger Equations with Linear Multiplicative Noise: Rescaling Approach. &lt;em&gt;Journal of Nonlinear Science&lt;/em&gt;. 2014;24(3):383-409.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W582670608","https://openalex.org/W621351040","https://openalex.org/W1542004730","https://openalex.org/W1559694286","https://openalex.org/W1606424902","https://openalex.org/W1672243955","https://openalex.org/W1980351659","https://openalex.org/W2007591148","https://openalex.org/W2022150597","https://openalex.org/W2023145735","https://openalex.org/W2077128690","https://openalex.org/W2085967987","https://openalex.org/W2091340876","https://openalex.org/W2094453790","https://openalex.org/W2101528443","https://openalex.org/W2117991721","https://openalex.org/W2171564961","https://openalex.org/W2495728325","https://openalex.org/W2594402535","https://openalex.org/W3098987883","https://openalex.org/W3101306265","https://openalex.org/W3102314118","https://openalex.org/W4292689972"],"related_works":["https://openalex.org/W2100121758","https://openalex.org/W3022718941","https://openalex.org/W4287812451","https://openalex.org/W1996414039","https://openalex.org/W2506602630","https://openalex.org/W3097284316","https://openalex.org/W2332961228","https://openalex.org/W2245214771","https://openalex.org/W2333053900","https://openalex.org/W1975562467"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
