{"id":"https://openalex.org/W4406422185","doi":"https://doi.org/10.3390/sym17010125","title":"On Superization of Nonlinear Integrable Dynamical Systems","display_name":"On Superization of Nonlinear Integrable Dynamical Systems","publication_year":2025,"publication_date":"2025-01-15","ids":{"openalex":"https://openalex.org/W4406422185","doi":"https://doi.org/10.3390/sym17010125"},"language":"en","primary_location":{"id":"doi:10.3390/sym17010125","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010125","pdf_url":"https://www.mdpi.com/2073-8994/17/1/125/pdf?version=1736952162","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/1/125/pdf?version=1736952162","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112459338","display_name":"Anatolij K. Prykarpatski","orcid":"https://orcid.org/0000-0001-5124-5890"},"institutions":[{"id":"https://openalex.org/I24881138","display_name":"Cracow University of Technology","ror":"https://ror.org/00pdej676","country_code":"PL","type":"education","lineage":["https://openalex.org/I24881138"]},{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["PL","UA"],"is_corresponding":true,"raw_author_name":"Anatolij K. Prykarpatski","raw_affiliation_strings":["Department of Advanced Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine","Department of Computer Science and Telecommunication, Cracow University of Technology, 31-155 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Advanced Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]},{"raw_affiliation_string":"Department of Computer Science and Telecommunication, Cracow University of Technology, 31-155 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I24881138"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074802886","display_name":"R. A. Kycia","orcid":"https://orcid.org/0000-0002-6390-4627"},"institutions":[{"id":"https://openalex.org/I24881138","display_name":"Cracow University of Technology","ror":"https://ror.org/00pdej676","country_code":"PL","type":"education","lineage":["https://openalex.org/I24881138"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Rados\u0142aw A. Kycia","raw_affiliation_strings":["Department of Computer Science and Telecommunication, Cracow University of Technology, 31-155 Krak\u00f3w, Poland"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Telecommunication, Cracow University of Technology, 31-155 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I24881138"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089166184","display_name":"V. Dilnyi","orcid":null},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Volodymyr M. Dilnyi","raw_affiliation_strings":["Department of Advanced Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine"],"affiliations":[{"raw_affiliation_string":"Department of Advanced Mathematics, Lviv Polytechnic National University, 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112459338"],"corresponding_institution_ids":["https://openalex.org/I24881138","https://openalex.org/I98435010"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":4.2898,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.92649668,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"17","issue":"1","first_page":"125","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9977999925613403,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9973999857902527,"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/integrable-system","display_name":"Integrable system","score":0.7460454106330872},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6230895519256592},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5251635909080505},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"Nonlinear dynamical systems","score":0.47638243436813354},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4424739480018616},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.40017762780189514},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3918033540248871},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3536830246448517},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3393040895462036},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.334301620721817},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2295360565185547},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1481626033782959},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11600667238235474},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08629938960075378}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7460454106330872},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6230895519256592},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5251635909080505},{"id":"https://openalex.org/C2983030100","wikidata":"https://www.wikidata.org/wiki/Q638328","display_name":"Nonlinear dynamical systems","level":3,"score":0.47638243436813354},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4424739480018616},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40017762780189514},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3918033540248871},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3536830246448517},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3393040895462036},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.334301620721817},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2295360565185547},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1481626033782959},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11600667238235474},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08629938960075378}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17010125","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010125","pdf_url":"https://www.mdpi.com/2073-8994/17/1/125/pdf?version=1736952162","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:225b88c841b04ed7bd17ea9c698c29b5","is_oa":true,"landing_page_url":"https://doaj.org/article/225b88c841b04ed7bd17ea9c698c29b5","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 17, Iss 1, p 125 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym17010125","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17010125","pdf_url":"https://www.mdpi.com/2073-8994/17/1/125/pdf?version=1736952162","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406422185.pdf"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W79822578","https://openalex.org/W1500463740","https://openalex.org/W1583700021","https://openalex.org/W1837101491","https://openalex.org/W1966079685","https://openalex.org/W1970567173","https://openalex.org/W1973107894","https://openalex.org/W1978592966","https://openalex.org/W1982416338","https://openalex.org/W1987477699","https://openalex.org/W1989612317","https://openalex.org/W1992123408","https://openalex.org/W1999572526","https://openalex.org/W2006123843","https://openalex.org/W2006213657","https://openalex.org/W2011703594","https://openalex.org/W2011707175","https://openalex.org/W2012206042","https://openalex.org/W2012663946","https://openalex.org/W2013031807","https://openalex.org/W2024558268","https://openalex.org/W2025274521","https://openalex.org/W2032875321","https://openalex.org/W2037552432","https://openalex.org/W2050952420","https://openalex.org/W2057660906","https://openalex.org/W2060407103","https://openalex.org/W2065762925","https://openalex.org/W2078882818","https://openalex.org/W2084596047","https://openalex.org/W2089453974","https://openalex.org/W2093785095","https://openalex.org/W2119310340","https://openalex.org/W2154435402","https://openalex.org/W2165004454","https://openalex.org/W2317740332","https://openalex.org/W2406944101","https://openalex.org/W2480162062","https://openalex.org/W2575702259","https://openalex.org/W2930342612","https://openalex.org/W2963097980","https://openalex.org/W2991006246","https://openalex.org/W3098996806","https://openalex.org/W3101844487","https://openalex.org/W3102434188","https://openalex.org/W4211028366","https://openalex.org/W4211036616","https://openalex.org/W4224435946","https://openalex.org/W4234144990","https://openalex.org/W6603307000","https://openalex.org/W6628746039","https://openalex.org/W6675045584"],"related_works":["https://openalex.org/W2051254274","https://openalex.org/W2056626217","https://openalex.org/W1541871911","https://openalex.org/W1966008566","https://openalex.org/W2184005427","https://openalex.org/W3185784018","https://openalex.org/W2079574545","https://openalex.org/W3127651486","https://openalex.org/W2050258033","https://openalex.org/W2148316232"],"abstract_inverted_index":{"We":[0,43],"study":[1],"an":[2,15],"interesting":[3],"superization":[4,53,101,107],"problem":[5],"of":[6,54,87,108,115,121,131],"integrable":[7,35,90],"nonlinear":[8,91],"dynamical":[9,75,92],"systems":[10,93],"on":[11,24,38,51,94,124,134],"functional":[12,41,69],"manifolds.":[13],"As":[14],"example,":[16],"we":[17,79],"considered":[18],"a":[19,33,39,84,100,105],"quantum":[20],"many-particle":[21],"Schr\u00f6dinger\u2013Davydov":[22],"model":[23],"the":[25,46,52,55,62,67,74,109,118,125,128,135],"axis,":[26],"whose":[27],"quasi-classical":[28],"reduction":[29],"proved":[30],"to":[31,72,98,127],"be":[32],"completely":[34],"Hamiltonian":[36],"system":[37,76],"smooth":[40],"manifold.":[42],"checked":[44],"that":[45,81],"so-called":[47],"\u201cnaive\u201d":[48],"approach,":[49],"based":[50],"related":[56,68,110],"phase":[57],"space":[58],"variables":[59],"via":[60],"extending":[61],"corresponding":[63,129],"Poisson":[64],"brackets":[65],"upon":[66],"supermanifold,":[70],"fails":[71],"retain":[73],"super-integrability.":[77],"Moreover,":[78],"demonstrated":[80],"there":[82],"exists":[83],"wide":[85],"class":[86],"classical":[88],"Lax-type":[89,111],"axes":[95],"in":[96,104],"relation":[97],"which":[99],"scheme":[102],"consists":[103],"reasonable":[106],"representation":[112],"by":[113],"means":[114],"passing":[116],"from":[117],"basic":[119],"algebra":[120],"pseudo-differential":[122],"operators":[123,133],"axis":[126],"superalgebra":[130],"super-pseudodifferential":[132],"superaxis.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-03-11T06:11:40.159057","created_date":"2025-10-10T00:00:00"}