{"id":"https://openalex.org/W2082008331","doi":"https://doi.org/10.1063/1.533071","title":"B\u00e4cklund transformation and its superposition principle of a Blaszak\u2013Marciniak four-field lattice","display_name":"B\u00e4cklund transformation and its superposition principle of a Blaszak\u2013Marciniak four-field lattice","publication_year":1999,"publication_date":"1999-11-01","ids":{"openalex":"https://openalex.org/W2082008331","doi":"https://doi.org/10.1063/1.533071","mag":"2082008331"},"language":"en","primary_location":{"id":"doi:10.1063/1.533071","doi":"https://doi.org/10.1063/1.533071","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.533071","pdf_url":null,"source":{"id":"https://openalex.org/S158241587","display_name":"Journal of Mathematical Physics","issn_l":"0022-2488","issn":["0022-2488","1089-7658","1527-2427"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043445257","display_name":"Wen-Xiu Ma","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wen-Xiu Ma","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100838529","display_name":"Xing\u2010Biao Hu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4391767993","display_name":"State Key Laboratory of Scientific and Engineering Computing","ror":"https://ror.org/02fp7dp35","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485","https://openalex.org/I4391767993"]},{"id":"https://openalex.org/I51296178","display_name":"China Center of Advanced Science and Technology","ror":"https://ror.org/02egfyg20","country_code":"CN","type":"facility","lineage":["https://openalex.org/I102398690","https://openalex.org/I4210122102","https://openalex.org/I51296178"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xing-Biao Hu","raw_affiliation_strings":["CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, People\u2019s Republic of China","State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific Engineering Computing, Academia Sinica, P.O. Box 2719, Beijing 100080, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CCAST (World Laboratory), P.O. Box 8730, Beijing 100080, People\u2019s Republic of China","institution_ids":["https://openalex.org/I51296178"]},{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific Engineering Computing, Academia Sinica, P.O. Box 2719, Beijing 100080, People\u2019s Republic of China","institution_ids":["https://openalex.org/I4391767993"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112118314","display_name":"Siming Zhu","orcid":"https://orcid.org/0009-0002-3588-7337","observed_orcids":["https://orcid.org/0009-0002-3588-7337","https://orcid.org/0000-0001-8270-7314"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Si-Ming Zhu","raw_affiliation_strings":["Department of Mathematics, Zhongshan University, Guangzhou 510275, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhongshan University, Guangzhou 510275, People\u2019s Republic of China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041635660","display_name":"Yongtang Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yong-Tang Wu","raw_affiliation_strings":["Department of Computer Science, Hong Kong Baptist University, Kowloon, Hong Kong, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Hong Kong Baptist University, Kowloon, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I141568987"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6585,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.84551114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"40","issue":"11","first_page":"6071","last_page":"6086"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0,"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/backlund-transformations","display_name":"B\u00e4cklund transformations","score":0.9520000219345093},{"id":"https://openalex.org/keywords/superposition","display_name":"superposition","score":0.777999997138977},{"id":"https://openalex.org/keywords/bilinear-forms","display_name":"bilinear forms","score":0.8190000057220459},{"id":"https://openalex.org/keywords/auxiliary-variables","display_name":"auxiliary variables","score":0.6209999918937683},{"id":"https://openalex.org/keywords/nonlinear-superposition-formula","display_name":"nonlinear superposition formula","score":0.9120000004768372},{"id":"https://openalex.org/keywords/soliton-solutions","display_name":"soliton solutions","score":0.9760000109672546},{"id":"https://openalex.org/keywords/integrable-lattices","display_name":"integrable lattices","score":0.7590000033378601}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.6799889802932739},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6594346761703491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6409974098205566},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.5451913475990295},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.5037257075309753},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4880481958389282},{"id":"https://openalex.org/C8828549","wikidata":"https://www.wikidata.org/wiki/Q837924","display_name":"Bilinear form","level":2,"score":0.4718492031097412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3449223041534424},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.27043259143829346},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.20664486289024353},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1063/1.533071","doi":"https://doi.org/10.1063/1.533071","is_oa":false,"landing_page_url":"https://doi.org/10.1063/1.533071","pdf_url":null,"source":{"id":"https://openalex.org/S158241587","display_name":"Journal of Mathematical Physics","issn_l":"0022-2488","issn":["0022-2488","1089-7658","1527-2427"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310320257","host_organization_name":"American Institute of Physics","host_organization_lineage":["https://openalex.org/P4310320257"],"host_organization_lineage_names":["American Institute of Physics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Mathematical Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W398431032","https://openalex.org/W1966738436","https://openalex.org/W1972853772","https://openalex.org/W2012836972","https://openalex.org/W2083498778","https://openalex.org/W2089148957","https://openalex.org/W2090908237","https://openalex.org/W2112133594","https://openalex.org/W2133243254","https://openalex.org/W2799225279","https://openalex.org/W4253110154"],"related_works":["https://openalex.org/W4200053212","https://openalex.org/W2235548299","https://openalex.org/W4220877270","https://openalex.org/W1963546854","https://openalex.org/W2197675418","https://openalex.org/W2357064270","https://openalex.org/W1976845455","https://openalex.org/W4306710942","https://openalex.org/W1987107190","https://openalex.org/W2031905258"],"abstract_inverted_index":{"A":[0,19],"four-field":[1],"lattice":[2,29,46],"furnished":[3],"by":[4],"Blaszak":[5],"and":[6,30],"Marciniak":[7],"is":[8,25,36],"transformed":[9],"into":[10],"bilinear":[11,23],"form":[12,24],"upon":[13],"introducing":[14],"two":[15],"auxiliary":[16],"independent":[17],"variables.":[18],"B\u00e4cklund":[20],"transformation":[21],"in":[22],"found":[26],"for":[27],"the":[28,31,45],"corresponding":[32],"nonlinear":[33],"superposition":[34],"formula":[35],"rigorously":[37],"established.":[38],"As":[39],"a":[40],"consequence,":[41],"soliton":[42],"solutions":[43],"to":[44],"are":[47],"derived.":[48]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-09-24T07:57:37.273135","created_date":"2025-10-10T00:00:00"}