{"id":"https://openalex.org/W3202988350","doi":"https://doi.org/10.3390/sym13101827","title":"Surfaces and Curves Induced by Nonlinear Schr\u00f6dinger-Type Equations and Their Spin Systems","display_name":"Surfaces and Curves Induced by Nonlinear Schr\u00f6dinger-Type Equations and Their Spin Systems","publication_year":2021,"publication_date":"2021-09-30","ids":{"openalex":"https://openalex.org/W3202988350","doi":"https://doi.org/10.3390/sym13101827","mag":"3202988350"},"language":"en","primary_location":{"id":"doi:10.3390/sym13101827","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101827","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1827/pdf?version=1634026710","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/2073-8994/13/10/1827/pdf?version=1634026710","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055679888","display_name":"Akbota Myrzakul","orcid":null},"institutions":[{"id":"https://openalex.org/I10232997","display_name":"L. N. Gumilyov Eurasian National University","ror":"https://ror.org/0242cby63","country_code":"KZ","type":"education","lineage":["https://openalex.org/I10232997"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Akbota Myrzakul","raw_affiliation_strings":["Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]},{"raw_affiliation_string":"Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049281206","display_name":"Gulgassyl Nugmanova","orcid":"https://orcid.org/0000-0002-4492-2459"},"institutions":[{"id":"https://openalex.org/I10232997","display_name":"L. N. Gumilyov Eurasian National University","ror":"https://ror.org/0242cby63","country_code":"KZ","type":"education","lineage":["https://openalex.org/I10232997"]}],"countries":["KZ"],"is_corresponding":true,"raw_author_name":"Gulgassyl Nugmanova","raw_affiliation_strings":["Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]},{"raw_affiliation_string":"Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019064328","display_name":"Nurzhan Serikbayev","orcid":"https://orcid.org/0000-0002-1259-637X"},"institutions":[{"id":"https://openalex.org/I10232997","display_name":"L. N. Gumilyov Eurasian National University","ror":"https://ror.org/0242cby63","country_code":"KZ","type":"education","lineage":["https://openalex.org/I10232997"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Nurzhan Serikbayev","raw_affiliation_strings":["Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]},{"raw_affiliation_string":"Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058341975","display_name":"Ratbay Myrzakulov","orcid":"https://orcid.org/0000-0002-5274-0815"},"institutions":[{"id":"https://openalex.org/I10232997","display_name":"L. N. Gumilyov Eurasian National University","ror":"https://ror.org/0242cby63","country_code":"KZ","type":"education","lineage":["https://openalex.org/I10232997"]}],"countries":["KZ"],"is_corresponding":false,"raw_author_name":"Ratbay Myrzakulov","raw_affiliation_strings":["Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]},{"raw_affiliation_string":"Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, Nur-Sultan 010009, Kazakhstan","institution_ids":["https://openalex.org/I10232997"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5049281206"],"corresponding_institution_ids":["https://openalex.org/I10232997"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0498,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.76862989,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"13","issue":"10","first_page":"1827","last_page":"1827"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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":1.0,"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":0.9988999962806702,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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":0.8352144956588745},{"id":"https://openalex.org/keywords/differential-geometry-of-curves","display_name":"Differential geometry of curves","score":0.6154506206512451},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5853481292724609},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5007755756378174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4864034950733185},{"id":"https://openalex.org/keywords/spin","display_name":"Spin (aerodynamics)","score":0.44943559169769287},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44943416118621826},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4435674846172333},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.43975770473480225},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.40232768654823303},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3512202203273773},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.24126291275024414},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2101699709892273},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.17359238862991333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11990153789520264}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.8352144956588745},{"id":"https://openalex.org/C194596105","wikidata":"https://www.wikidata.org/wiki/Q2254404","display_name":"Differential geometry of curves","level":5,"score":0.6154506206512451},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5853481292724609},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5007755756378174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4864034950733185},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.44943559169769287},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44943416118621826},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4435674846172333},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.43975770473480225},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40232768654823303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3512202203273773},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.24126291275024414},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2101699709892273},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.17359238862991333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11990153789520264},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13101827","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101827","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1827/pdf?version=1634026710","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:bc76db103467473da1c85f66adda8722","is_oa":true,"landing_page_url":"https://doaj.org/article/bc76db103467473da1c85f66adda8722","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 10, p 1827 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/10/1827/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13101827","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13101827","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101827","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1827/pdf?version=1634026710","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3202988350.pdf","grobid_xml":"https://content.openalex.org/works/W3202988350.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W108936248","https://openalex.org/W1447479685","https://openalex.org/W1494563177","https://openalex.org/W1664880672","https://openalex.org/W1828216199","https://openalex.org/W1910698074","https://openalex.org/W1943544683","https://openalex.org/W1966865787","https://openalex.org/W1968792300","https://openalex.org/W1971096953","https://openalex.org/W1976409510","https://openalex.org/W1982139954","https://openalex.org/W1985266253","https://openalex.org/W1986272323","https://openalex.org/W1989427271","https://openalex.org/W1991863836","https://openalex.org/W1994399854","https://openalex.org/W1996240629","https://openalex.org/W2005947062","https://openalex.org/W2015179695","https://openalex.org/W2015814026","https://openalex.org/W2018969241","https://openalex.org/W2020462487","https://openalex.org/W2022848732","https://openalex.org/W2024573212","https://openalex.org/W2028865453","https://openalex.org/W2032785697","https://openalex.org/W2050390239","https://openalex.org/W2051375842","https://openalex.org/W2061460511","https://openalex.org/W2063368966","https://openalex.org/W2066252005","https://openalex.org/W2118551292","https://openalex.org/W2118575947","https://openalex.org/W2164454130","https://openalex.org/W2170290284","https://openalex.org/W2314520473","https://openalex.org/W2466135675","https://openalex.org/W2531289303","https://openalex.org/W2538976595","https://openalex.org/W2737235521","https://openalex.org/W2897194640","https://openalex.org/W2914810627","https://openalex.org/W2964073978","https://openalex.org/W2994579279","https://openalex.org/W3012307923","https://openalex.org/W3034378757","https://openalex.org/W3035454438","https://openalex.org/W3094748071","https://openalex.org/W3099399044","https://openalex.org/W3099814360","https://openalex.org/W3100594644","https://openalex.org/W3101154942","https://openalex.org/W3101431041","https://openalex.org/W3102217118","https://openalex.org/W3103821657","https://openalex.org/W3104441056","https://openalex.org/W3104571144","https://openalex.org/W3105975662","https://openalex.org/W3165445341","https://openalex.org/W3169552385","https://openalex.org/W3205311254","https://openalex.org/W4235322506","https://openalex.org/W6649443301","https://openalex.org/W6655091994"],"related_works":["https://openalex.org/W2317560809","https://openalex.org/W2383169266","https://openalex.org/W1576711457","https://openalex.org/W1549461434","https://openalex.org/W1001150892","https://openalex.org/W2043930649","https://openalex.org/W2056619336","https://openalex.org/W3216718091","https://openalex.org/W4294660533","https://openalex.org/W2148310704"],"abstract_inverted_index":{"In":[0,61,79],"recent":[1],"years,":[2],"symmetry":[3,67],"in":[4,13,51],"abstract":[5],"partial":[6],"differential":[7,69,190],"equations":[8,29,44,94,128,172],"has":[9],"found":[10],"wide":[11],"application":[12],"the":[14,23,36,66,83,89,97,115,120,125,140,152,155,158,163,174,186,189,199],"field":[15],"of":[16,22,48,71,109,157,192],"nonlinear":[17,42,91,126],"integrable":[18,43,75,165,180,195],"equations.":[19],"The":[20],"symmetries":[21],"corresponding":[24],"transformation":[25],"groups":[26],"for":[27,38,144,154,173,198],"such":[28],"make":[30],"it":[31],"possible":[32],"to":[33,56,104],"significantly":[34],"simplify":[35],"procedure":[37],"establishing":[39],"equivalence":[40,87],"between":[41,68,88,188],"from":[45],"different":[46],"areas":[47],"physics,":[49],"which":[50],"turn":[52],"open":[53],"up":[54],"opportunities":[55],"easily":[57],"find":[58],"their":[59],"solutions.":[60],"this":[62],"paper,":[63],"we":[64,81,118,184],"study":[65],"geometry":[70,191],"surfaces/curves":[72],"and":[73,85,96,129,167,194],"some":[74],"generalized":[76],"spin":[77,132,181,196],"systems.":[78,133,182],"particular,":[80],"investigate":[82,105],"gauge":[84],"geometrical":[86],"local/nonlocal":[90],"Schr\u00f6dinger":[92],"type":[93],"(NLSE)":[95],"extended":[98],"continuous":[99],"Heisenberg":[100],"ferromagnet":[101],"equation":[102,142,153],"(HFE)":[103],"how":[106],"nonlocality":[107],"properties":[108],"one":[110],"system":[111],"are":[112,137],"inherited":[113],"by":[114,124,139],"other.":[116],"First,":[117],"consider":[119],"space":[121,135],"curves":[122,136],"induced":[123],"Schr\u00f6dinger-type":[127],"its":[130,168],"equivalent":[131],"Such":[134],"governed":[138],"Serret\u2013Frenet":[141],"(SFE)":[143],"three":[145,200],"basis":[146,159,201],"vectors.":[147,202],"We":[148],"also":[149],"show":[150],"that":[151],"third":[156],"vectors":[160,177],"coincides":[161],"with":[162],"well-known":[164],"HFE":[166],"generalization.":[169],"Two":[170],"other":[171],"remaining":[175],"two":[176],"give":[178],"new":[179],"Finally,":[183],"investigated":[185],"relation":[187],"surfaces":[193],"systems":[197]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
