{"id":"https://openalex.org/W4400774033","doi":"https://doi.org/10.3390/axioms13070481","title":"Integrable Couplings and Two-Dimensional Unital Algebras","display_name":"Integrable Couplings and Two-Dimensional Unital Algebras","publication_year":2024,"publication_date":"2024-07-18","ids":{"openalex":"https://openalex.org/W4400774033","doi":"https://doi.org/10.3390/axioms13070481"},"language":"en","primary_location":{"id":"doi:10.3390/axioms13070481","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070481","pdf_url":"https://www.mdpi.com/2075-1680/13/7/481/pdf?version=1721297166","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/2075-1680/13/7/481/pdf?version=1721297166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062594909","display_name":"Wen\u2010Xiu Ma","orcid":"https://orcid.org/0000-0001-5309-1493"},"institutions":[{"id":"https://openalex.org/I135237710","display_name":"Zhejiang Normal University","ror":"https://ror.org/01vevwk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I135237710"]},{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]},{"id":"https://openalex.org/I2613432","display_name":"University of South Florida","ror":"https://ror.org/032db5x82","country_code":"US","type":"education","lineage":["https://openalex.org/I2613432"]},{"id":"https://openalex.org/I27765905","display_name":"North-West University","ror":"https://ror.org/010f1sq29","country_code":"ZA","type":"education","lineage":["https://openalex.org/I27765905"]}],"countries":["CN","SA","US","ZA"],"is_corresponding":true,"raw_author_name":"Wen-Xiu Ma","raw_affiliation_strings":["Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA","Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia","Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China","Material Science Innovation and Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA","institution_ids":["https://openalex.org/I2613432"]},{"raw_affiliation_string":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Material Science Innovation and Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa","institution_ids":["https://openalex.org/I27765905"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5062594909"],"corresponding_institution_ids":["https://openalex.org/I135237710","https://openalex.org/I185163786","https://openalex.org/I2613432","https://openalex.org/I27765905"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":9.9823,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9902873,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"13","issue":"7","first_page":"481","last_page":"481"},"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":0.9991999864578247,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unital","display_name":"Unital","score":0.9106500148773193},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.6900946497917175},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4456155300140381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4088134765625},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38139235973358154}],"concepts":[{"id":"https://openalex.org/C160873635","wikidata":"https://www.wikidata.org/wiki/Q17148807","display_name":"Unital","level":3,"score":0.9106500148773193},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.6900946497917175},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4456155300140381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4088134765625},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38139235973358154}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms13070481","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070481","pdf_url":"https://www.mdpi.com/2075-1680/13/7/481/pdf?version=1721297166","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:e385875b7e954ebd83a994a4e5bd92af","is_oa":true,"landing_page_url":"https://doaj.org/article/e385875b7e954ebd83a994a4e5bd92af","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":"Axioms, Vol 13, Iss 7, p 481 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms13070481","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms13070481","pdf_url":"https://www.mdpi.com/2075-1680/13/7/481/pdf?version=1721297166","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/G1182344820","display_name":null,"funder_award_id":"12271488","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5371501680","display_name":null,"funder_award_id":"11975145","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7125411293","display_name":null,"funder_award_id":"11972291","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8050651220","display_name":null,"funder_award_id":"202101","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4400774033.pdf","grobid_xml":"https://content.openalex.org/works/W4400774033.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1631607997","https://openalex.org/W1969429376","https://openalex.org/W1975042115","https://openalex.org/W1976969630","https://openalex.org/W1979823253","https://openalex.org/W1985727912","https://openalex.org/W1989901731","https://openalex.org/W1993439351","https://openalex.org/W2015208000","https://openalex.org/W2017153285","https://openalex.org/W2026028365","https://openalex.org/W2033047171","https://openalex.org/W2043531989","https://openalex.org/W2054884041","https://openalex.org/W2056317780","https://openalex.org/W2057776684","https://openalex.org/W2058003062","https://openalex.org/W2064828907","https://openalex.org/W2067176362","https://openalex.org/W2068705912","https://openalex.org/W2071914555","https://openalex.org/W2145187298","https://openalex.org/W2161475106","https://openalex.org/W2437151423","https://openalex.org/W2980776103","https://openalex.org/W3105345032","https://openalex.org/W3208658877","https://openalex.org/W4281641504","https://openalex.org/W4385144928","https://openalex.org/W4394757703","https://openalex.org/W4396806581","https://openalex.org/W4396901552","https://openalex.org/W6642668213","https://openalex.org/W6643861224","https://openalex.org/W6645380299","https://openalex.org/W6654067825","https://openalex.org/W6666687136","https://openalex.org/W6855352993"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W3103104364","https://openalex.org/W2972822140","https://openalex.org/W2044787408","https://openalex.org/W4249228129","https://openalex.org/W2060494588","https://openalex.org/W2086585817","https://openalex.org/W4394635378","https://openalex.org/W2019140719","https://openalex.org/W155593081"],"abstract_inverted_index":{"The":[0,25],"paper":[1],"aims":[2],"to":[3,52],"demonstrate":[4],"that":[5],"a":[6,10,19,30],"linear":[7],"expansion":[8],"in":[9],"unital":[11],"two-dimensional":[12],"algebra":[13],"can":[14],"generate":[15],"integrable":[16,26,37],"couplings,":[17],"proposing":[18],"novel":[20],"approach":[21],"for":[22],"their":[23],"construction.":[24],"couplings":[27],"presented":[28],"encompass":[29],"range":[31],"of":[32,60],"perturbation":[33],"equations":[34,63],"and":[35,43,56],"nonlinear":[36,61],"couplings.":[38],"Their":[39],"corresponding":[40],"Lax":[41],"pairs":[42],"hereditary":[44],"recursion":[45],"operators":[46],"are":[47,64],"explicitly":[48],"detailed.":[49],"Concrete":[50],"applications":[51],"the":[53,57],"KdV":[54],"equation":[55],"AKNS":[58],"system":[59],"Schr\u00f6dinger":[62],"extensively":[65],"explored.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":20}],"updated_date":"2026-03-22T08:09:32.410652","created_date":"2025-10-10T00:00:00"}
