{"id":"https://openalex.org/W4396558083","doi":"https://doi.org/10.1155/2024/5533472","title":"New Multilinear Variable Separation Solutions of the (3 + 1)-Dimensional Burgers Hierarchy","display_name":"New Multilinear Variable Separation Solutions of the (3 + 1)-Dimensional Burgers Hierarchy","publication_year":2024,"publication_date":"2024-04-30","ids":{"openalex":"https://openalex.org/W4396558083","doi":"https://doi.org/10.1155/2024/5533472"},"language":"en","primary_location":{"id":"doi:10.1155/2024/5533472","doi":"https://doi.org/10.1155/2024/5533472","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1155/2024/5533472","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2024/5533472","source":{"id":"https://openalex.org/S69511584","display_name":"Advances in Mathematical Physics","issn_l":"1687-9120","issn":["1687-9120","1687-9139"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematical Physics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4396558083"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2024/5533472","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102989844","display_name":"Wei Guo Zhu","orcid":"https://orcid.org/0000-0003-4731-0949","observed_orcids":["https://orcid.org/0000-0003-4731-0949"]},"institutions":[{"id":"https://openalex.org/I4210123686","display_name":"Quzhou University","ror":"https://ror.org/024nfx323","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210123686"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Zhu","raw_affiliation_strings":["College of Teacher Education, Quzhou University, Quzhou 324000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Teacher Education, Quzhou University, Quzhou 324000, China","institution_ids":["https://openalex.org/I4210123686"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100630871","display_name":"Jianyong Wang","orcid":"https://orcid.org/0000-0003-1689-2384","observed_orcids":["https://orcid.org/0000-0003-1689-2384"]},"institutions":[{"id":"https://openalex.org/I4210123686","display_name":"Quzhou University","ror":"https://ror.org/024nfx323","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210123686"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian-Yong Wang","raw_affiliation_strings":["College of Teacher Education, Quzhou University, Quzhou 324000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Teacher Education, Quzhou University, Quzhou 324000, China","institution_ids":["https://openalex.org/I4210123686"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100628895","display_name":"Kai Zhou","orcid":"https://orcid.org/0000-0002-1463-1829","observed_orcids":["https://orcid.org/0000-0002-1463-1829"]},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Zhou","raw_affiliation_strings":["Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081812062","display_name":"Shoufeng Shen","orcid":"https://orcid.org/0000-0003-2573-0686","observed_orcids":["https://orcid.org/0000-0003-2573-0686"]},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shoufeng Shen","raw_affiliation_strings":["Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"],"raw_orcid":"https://orcid.org/0000-0003-2573-0686","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China","institution_ids":["https://openalex.org/I55712492"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012580940","display_name":"Bo Ren","orcid":"https://orcid.org/0000-0002-3534-7528","observed_orcids":["https://orcid.org/0000-0002-3534-7528"]},"institutions":[{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Ren","raw_affiliation_strings":["Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"],"raw_orcid":"https://orcid.org/0000-0002-3534-7528","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China","institution_ids":["https://openalex.org/I55712492"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012580940"],"corresponding_institution_ids":["https://openalex.org/I55712492"],"apc_list":{"value":2450,"currency":"USD","value_usd":2450},"apc_paid":{"value":2450,"currency":"USD","value_usd":2450},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2024","issue":null,"first_page":"1","last_page":"7"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.0,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/exact-solutions","display_name":"exact solutions","score":0.8930000066757202},{"id":"https://openalex.org/keywords/soliton-interaction","display_name":"soliton interaction","score":0.9359999895095825},{"id":"https://openalex.org/keywords/coherent-structures","display_name":"coherent structures","score":0.9269999861717224},{"id":"https://openalex.org/keywords/jimbo-miwa-equation","display_name":"Jimbo-Miwa equation","score":0.9150000214576721},{"id":"https://openalex.org/keywords/integrable-systems","display_name":"integrable systems","score":0.8450000286102295}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.884186327457428},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.865166425704956},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7573304176330566},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.626943826675415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.575776219367981},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.5612828731536865},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5333250761032104},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4894022047519684},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4700823128223419},{"id":"https://openalex.org/C159722891","wikidata":"https://www.wikidata.org/wiki/Q913323","display_name":"Separation of variables","level":3,"score":0.4642624855041504},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.46225422620773315},{"id":"https://openalex.org/C175205982","wikidata":"https://www.wikidata.org/wiki/Q208920","display_name":"One-dimensional space","level":2,"score":0.4486161768436432},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4206979274749756},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.303544282913208},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.18217375874519348},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1557287573814392},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06379452347755432},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06362926959991455},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.051493555307388306},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2024/5533472","doi":"https://doi.org/10.1155/2024/5533472","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1155/2024/5533472","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2024/5533472","source":{"id":"https://openalex.org/S69511584","display_name":"Advances in Mathematical Physics","issn_l":"1687-9120","issn":["1687-9120","1687-9139"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematical Physics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlamp:5533472","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/amp/2024/5533472.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:17dd11ee29bb412f8e0c9f0d7455b143","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/17dd11ee29bb412f8e0c9f0d7455b143","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,"listed_in":[],"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":"Advances in Mathematical Physics, Vol 2024 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2024/5533472","doi":"https://doi.org/10.1155/2024/5533472","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1155/2024/5533472","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/2024/5533472","source":{"id":"https://openalex.org/S69511584","display_name":"Advances in Mathematical Physics","issn_l":"1687-9120","issn":["1687-9120","1687-9139"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","norway-1","poland-40","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematical Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G5576404549","display_name":null,"funder_award_id":"12375006","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/W4396558083.pdf","grobid_xml":"https://content.openalex.org/works/W4396558083.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1969164483","https://openalex.org/W1974587970","https://openalex.org/W1989295244","https://openalex.org/W2002108603","https://openalex.org/W2017459334","https://openalex.org/W2021222035","https://openalex.org/W2024666336","https://openalex.org/W2034817918","https://openalex.org/W2039524934","https://openalex.org/W2052142989","https://openalex.org/W2071583727","https://openalex.org/W2300055079","https://openalex.org/W2396125236","https://openalex.org/W3134526257","https://openalex.org/W4223636762","https://openalex.org/W4225564649","https://openalex.org/W4281291912","https://openalex.org/W4296432523","https://openalex.org/W4383103504","https://openalex.org/W4384935239","https://openalex.org/W4385649192"],"related_works":["https://openalex.org/W2021222035","https://openalex.org/W2059644086","https://openalex.org/W1541289316","https://openalex.org/W2013546083","https://openalex.org/W2396125236","https://openalex.org/W1583362833","https://openalex.org/W3150005455","https://openalex.org/W2349489368","https://openalex.org/W870248018","https://openalex.org/W2327114498"],"abstract_inverted_index":{"The":[0],"multilinear":[1],"variable":[2],"separation":[3],"(MLVS)":[4],"approach":[5,34],"has":[6],"been":[7],"proven":[8],"to":[9,35,55],"be":[10],"very":[11],"useful":[12],"in":[13,73],"solving":[14],"(2":[15],"+":[16,23,41,58,84],"1)-dimensional":[17,24,42,59,85],"integrable":[18],"systems.":[19],"Taking":[20],"the":[21,32,78,82],"(3":[22,40,57,83],"Burgers":[25,43],"hierarchy":[26],"as":[27],"an":[28],"example,":[29],"we":[30],"extend":[31],"MLVS":[33,79],"a":[36],"whole":[37],"family":[38],"of":[39,81],"hierarchy.":[44],"New":[45],"exact":[46],"solutions":[47],"and":[48,68,89],"universal":[49],"formulas":[50],"are":[51,71],"obtained,":[52],"which":[53],"lead":[54],"abundant":[56],"coherent":[60],"structures.":[61],"In":[62],"particular,":[63],"two":[64],"ring-type":[65],"soliton":[66],"molecules":[67],"their":[69],"interactions":[70],"shown":[72],"detail.":[74],"We":[75],"also":[76],"generalize":[77],"results":[80],"Jimbo\u2013Miwa":[86],"(JM)":[87],"equation":[88],"modified":[90],"JM":[91],"equation.":[92]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2024-05-02T00:00:00"}
