{"id":"https://openalex.org/W4386304031","doi":"https://doi.org/10.3390/axioms12090840","title":"Using Vector-Product Loop Algebra to Generate Integrable Systems","display_name":"Using Vector-Product Loop Algebra to Generate Integrable Systems","publication_year":2023,"publication_date":"2023-08-29","ids":{"openalex":"https://openalex.org/W4386304031","doi":"https://doi.org/10.3390/axioms12090840"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12090840","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090840","pdf_url":"https://www.mdpi.com/2075-1680/12/9/840/pdf?version=1693322317","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/9/840/pdf?version=1693322317","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100410103","display_name":"Jian Zhang","orcid":"https://orcid.org/0000-0003-4995-6495"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Zhang","raw_affiliation_strings":["School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111693943","display_name":"Binlu Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I66883779","display_name":"Weifang University","ror":"https://ror.org/01frp7483","country_code":"CN","type":"education","lineage":["https://openalex.org/I66883779"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Binlu Feng","raw_affiliation_strings":["School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Information Sciences, Weifang University, Weifang 261061, China","institution_ids":["https://openalex.org/I66883779"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100459701","display_name":"Yufeng Zhang","orcid":"https://orcid.org/0000-0003-4461-5237"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yufeng Zhang","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084860301","display_name":"Long Ju","orcid":"https://orcid.org/0000-0002-4691-1315"},"institutions":[{"id":"https://openalex.org/I25757504","display_name":"China University of Mining and Technology","ror":"https://ror.org/01xt2dr21","country_code":"CN","type":"education","lineage":["https://openalex.org/I25757504"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Long Ju","raw_affiliation_strings":["School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China","institution_ids":["https://openalex.org/I25757504"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5111693943"],"corresponding_institution_ids":["https://openalex.org/I66883779"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.3152,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.53881056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"9","first_page":"840","last_page":"840"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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":0.9998999834060669,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9807999730110168,"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/isospectral","display_name":"Isospectral","score":0.917573869228363},{"id":"https://openalex.org/keywords/loop-algebra","display_name":"Loop algebra","score":0.8828932046890259},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.827973484992981},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6394730806350708},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5344193577766418},{"id":"https://openalex.org/keywords/multivector","display_name":"Multivector","score":0.4401259124279022},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39201653003692627},{"id":"https://openalex.org/keywords/current-algebra","display_name":"Current algebra","score":0.38907676935195923},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.17635667324066162}],"concepts":[{"id":"https://openalex.org/C2779710842","wikidata":"https://www.wikidata.org/wiki/Q6086323","display_name":"Isospectral","level":2,"score":0.917573869228363},{"id":"https://openalex.org/C2781197150","wikidata":"https://www.wikidata.org/wiki/Q17098626","display_name":"Loop algebra","level":4,"score":0.8828932046890259},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.827973484992981},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6394730806350708},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5344193577766418},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.4401259124279022},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39201653003692627},{"id":"https://openalex.org/C81999800","wikidata":"https://www.wikidata.org/wiki/Q1454725","display_name":"Current algebra","level":3,"score":0.38907676935195923},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.17635667324066162}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12090840","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090840","pdf_url":"https://www.mdpi.com/2075-1680/12/9/840/pdf?version=1693322317","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:25be2f29dae0461db73f0c4f9ed89845","is_oa":true,"landing_page_url":"https://doaj.org/article/25be2f29dae0461db73f0c4f9ed89845","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":"Axioms, Vol 12, Iss 9, p 840 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/9/840/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12090840","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":"Axioms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12090840","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12090840","pdf_url":"https://www.mdpi.com/2075-1680/12/9/840/pdf?version=1693322317","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4536593145","display_name":null,"funder_award_id":"11971475","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386304031.pdf","grobid_xml":"https://content.openalex.org/works/W4386304031.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W83763115","https://openalex.org/W1525018523","https://openalex.org/W1976026260","https://openalex.org/W1984800816","https://openalex.org/W1985411652","https://openalex.org/W1986406528","https://openalex.org/W1992619775","https://openalex.org/W1994034727","https://openalex.org/W1998237133","https://openalex.org/W2005064009","https://openalex.org/W2005457825","https://openalex.org/W2013673280","https://openalex.org/W2019740517","https://openalex.org/W2045864229","https://openalex.org/W2049662054","https://openalex.org/W2058091840","https://openalex.org/W2058269591","https://openalex.org/W2062656737","https://openalex.org/W2065648229","https://openalex.org/W2083370802","https://openalex.org/W2085413857","https://openalex.org/W2090505566","https://openalex.org/W2095315309","https://openalex.org/W2098396013","https://openalex.org/W2105115183","https://openalex.org/W2114369755","https://openalex.org/W2276419850","https://openalex.org/W2341743549","https://openalex.org/W2478895671","https://openalex.org/W2670283069","https://openalex.org/W2737706071","https://openalex.org/W2985063108","https://openalex.org/W3038085088","https://openalex.org/W3102922037","https://openalex.org/W3105997241","https://openalex.org/W3138162571","https://openalex.org/W3154035006","https://openalex.org/W3161707124","https://openalex.org/W3169574628","https://openalex.org/W3190370035","https://openalex.org/W4292170110","https://openalex.org/W4306769410","https://openalex.org/W4309542606","https://openalex.org/W6672043708"],"related_works":["https://openalex.org/W1979823253","https://openalex.org/W2371762260","https://openalex.org/W3135293428","https://openalex.org/W2378465642","https://openalex.org/W2244670214","https://openalex.org/W2010748370","https://openalex.org/W2092577538","https://openalex.org/W3083250665","https://openalex.org/W2368019203","https://openalex.org/W2053741851"],"abstract_inverted_index":{"A":[0],"new":[1,34,92,129,155],"three-dimensional":[2,118],"Lie":[3],"algebra":[4,8,120,125],"and":[5,25,58,74],"its":[6],"loop":[7,119,124],"are":[9,29],"proposed":[10],"by":[11,31,40],"us,":[12],"whose":[13,143],"commutator":[14],"is":[15,67,79,110,134,141,146],"a":[16,22,26,33,47,51,55,59,91,122,128,135],"vector":[17,42],"product.":[18],"Based":[19],"on":[20],"this,":[21],"positive":[23],"flow":[24,28],"negative":[27],"obtained":[30],"introducing":[32],"kind":[35],"of":[36,85,101,137,167,171],"spectral":[37],"problem":[38],"expressed":[39],"the":[41,63,86,98,102,108,117,150,159,165],"product,":[43],"which":[44,97,133],"reduces":[45],"to":[46,89],"generalized":[48,52,68],"KdV":[49],"equation,":[50,54,57],"Schr\u00f6dinger":[53],"sine-Gordon":[56],"sinh-Gordon":[60],"equation.":[61],"Next,":[62],"well-known":[64],"Tu":[65],"scheme":[66],"for":[69,96],"generating":[70,168],"isospectral":[71,103,130],"integrable":[72,76,104,131,139,169],"hierarchies":[73,170],"non-isospectral":[75],"hierarchies.":[77],"It":[78],"important":[80],"that":[81,127],"we":[82,114],"make":[83],"use":[84],"variational":[87],"method":[88],"create":[90],"vector-product":[93,151],"trace":[94,152],"identity":[95],"Hamiltonian":[99],"structure":[100,145],"hierarchy":[105,132],"presented":[106,157],"in":[107,158,164],"paper":[109,160],"worded":[111],"out.":[112],"Finally,":[113],"further":[115],"enlarge":[116],"into":[121],"six-dimensional":[123],"so":[126],"type":[136],"extended":[138],"model":[140],"produced":[142],"bi-Hamiltonian":[144],"also":[147],"derived":[148],"from":[149],"identity.":[153],"This":[154],"approach":[156],"possesses":[161],"extensive":[162],"applications":[163],"aspect":[166],"evolution":[172],"equations.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}