{"id":"https://openalex.org/W2982395998","doi":"https://doi.org/10.1155/2019/5479695","title":"Nonlocal Symmetry and B\u00e4cklund Transformation of a Negative\u2010Order Korteweg\u2013de Vries Equation","display_name":"Nonlocal Symmetry and B\u00e4cklund Transformation of a Negative\u2010Order Korteweg\u2013de Vries Equation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2982395998","doi":"https://doi.org/10.1155/2019/5479695","mag":"2982395998"},"language":"en","primary_location":{"id":"doi:10.1155/2019/5479695","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5479695","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/5479695.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2019/5479695.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083255119","display_name":"Jin-Xi Fei","orcid":null},"institutions":[{"id":"https://openalex.org/I3129496460","display_name":"Lishui University","ror":"https://ror.org/0418kp584","country_code":"CN","type":"education","lineage":["https://openalex.org/I3129496460"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinxi Fei","raw_affiliation_strings":["Institute of Optoelectronic Technology, Lishui University, Lishui 323000, China"],"affiliations":[{"raw_affiliation_string":"Institute of Optoelectronic Technology, Lishui University, Lishui 323000, China","institution_ids":["https://openalex.org/I3129496460"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041707818","display_name":"Wei\u2010Ping Cao","orcid":"https://orcid.org/0000-0002-9684-4835"},"institutions":[{"id":"https://openalex.org/I3129496460","display_name":"Lishui University","ror":"https://ror.org/0418kp584","country_code":"CN","type":"education","lineage":["https://openalex.org/I3129496460"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Weiping Cao","raw_affiliation_strings":["Institute of Optoelectronic Technology, Lishui University, Lishui 323000, China"],"affiliations":[{"raw_affiliation_string":"Institute of Optoelectronic Technology, Lishui University, Lishui 323000, China","institution_ids":["https://openalex.org/I3129496460"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068839211","display_name":"Zheng-Yi Ma","orcid":"https://orcid.org/0000-0002-5389-2052"},"institutions":[{"id":"https://openalex.org/I1328775524","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55","country_code":"CN","type":"education","lineage":["https://openalex.org/I1328775524"]},{"id":"https://openalex.org/I3129496460","display_name":"Lishui University","ror":"https://ror.org/0418kp584","country_code":"CN","type":"education","lineage":["https://openalex.org/I3129496460"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengyi Ma","raw_affiliation_strings":["Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China","Institute of Nonlinear Analysis and Department of Mathematics, Lishui University, Lishui 323000, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I1328775524"]},{"raw_affiliation_string":"Institute of Nonlinear Analysis and Department of Mathematics, Lishui University, Lishui 323000, China","institution_ids":["https://openalex.org/I3129496460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041707818"],"corresponding_institution_ids":["https://openalex.org/I3129496460"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.864,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74198047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2019","issue":"1","first_page":null,"last_page":null},"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":0.9966999888420105,"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/T12748","display_name":"Molecular spectroscopy and chirality","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.7411404848098755},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.6785537004470825},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6278627514839172},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.5800284743309021},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5223118662834167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4848107397556305},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4523582458496094},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2027590572834015},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10520204901695251},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09648290276527405},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.05426895618438721}],"concepts":[{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.7411404848098755},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.6785537004470825},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6278627514839172},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.5800284743309021},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5223118662834167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4848107397556305},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4523582458496094},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2027590572834015},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10520204901695251},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09648290276527405},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.05426895618438721},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2019/5479695","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5479695","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/5479695.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:5479695","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2019/5479695.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,"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:5d1b86cdbcac483b8ac186fcc4efd158","is_oa":true,"landing_page_url":"https://doaj.org/article/5d1b86cdbcac483b8ac186fcc4efd158","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/5479695","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5479695","pdf_url":"https://downloads.hindawi.com/journals/complexity/2019/5479695.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"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/G3009538320","display_name":null,"funder_award_id":"1177510","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/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5760752404","display_name":null,"funder_award_id":"Projects","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/G7608752429","display_name":null,"funder_award_id":"Talent","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8129418132","display_name":null,"funder_award_id":"11775104","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/W2982395998.pdf","grobid_xml":"https://content.openalex.org/works/W2982395998.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1979722387","https://openalex.org/W1980257099","https://openalex.org/W1981661253","https://openalex.org/W1990907100","https://openalex.org/W2017358916","https://openalex.org/W2017361495","https://openalex.org/W2034796287","https://openalex.org/W2044177847","https://openalex.org/W2061509202","https://openalex.org/W2062572188","https://openalex.org/W2078748927","https://openalex.org/W2094563325","https://openalex.org/W2161164203","https://openalex.org/W2590362739","https://openalex.org/W2612660319","https://openalex.org/W2743495047","https://openalex.org/W2749917866","https://openalex.org/W3098312223"],"related_works":["https://openalex.org/W2027202866","https://openalex.org/W3149920197","https://openalex.org/W4293569346","https://openalex.org/W2397056152","https://openalex.org/W2531671773","https://openalex.org/W2070026745","https://openalex.org/W3098850177","https://openalex.org/W2392521623","https://openalex.org/W2024710114","https://openalex.org/W2072641535"],"abstract_inverted_index":{"The":[0],"residual":[1,17,51,61],"symmetry":[2,18],"of":[3,59,76],"a":[4],"negative\u2010order":[5],"Korteweg\u2013de":[6],"Vries":[7],"(nKdV)":[8],"equation":[9,26,72],"is":[10,27],"derived":[11],"through":[12],"its":[13],"Lax":[14],"pair.":[15],"Such":[16],"can":[19],"be":[20],"localized,":[21],"and":[22,63],"the":[23,45,49,56,74,77],"original":[24],"nKdV":[25,71],"extended":[28],"into":[29],"an":[30],"enlarged":[31],"system":[32],"by":[33],"introducing":[34],"four":[35],"new":[36],"variables.":[37],"By":[38],"using":[39],"Lie\u2019s":[40],"first":[41],"theorem,":[42],"we":[43,54],"obtain":[44],"finite":[46],"transformation":[47,68],"for":[48,69],"localized":[50],"symmetry.":[52],"Furthermore,":[53],"localize":[55],"linear":[57],"superposition":[58],"multiple":[60],"symmetries":[62],"construct":[64],"n":[65],"\u2010th":[66],"B\u00e4cklund":[67],"this":[70],"in":[73],"form":[75],"determinants.":[78]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-20T07:46:08.049788","created_date":"2025-10-10T00:00:00"}