{"id":"https://openalex.org/W2026856494","doi":"https://doi.org/10.1142/s0217979214500672","title":"PAINLEV\u00c9 ANALYSIS AND NEW ANALYTIC SOLUTIONS FOR (1+1)-DIMENSIONAL HIGHER-ORDER BROER\u2013KAUP SYSTEM WITH SYMBOLIC COMPUTATION","display_name":"PAINLEV\u00c9 ANALYSIS AND NEW ANALYTIC SOLUTIONS FOR (1+1)-DIMENSIONAL HIGHER-ORDER BROER\u2013KAUP SYSTEM WITH SYMBOLIC COMPUTATION","publication_year":2014,"publication_date":"2014-02-18","ids":{"openalex":"https://openalex.org/W2026856494","doi":"https://doi.org/10.1142/s0217979214500672","mag":"2026856494"},"language":"en","primary_location":{"id":"doi:10.1142/s0217979214500672","doi":"https://doi.org/10.1142/s0217979214500672","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217979214500672","pdf_url":null,"source":{"id":"https://openalex.org/S130197424","display_name":"International Journal of Modern Physics B","issn_l":"0217-9792","issn":["0217-9792","1793-6578"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Physics B","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":null,"display_name":"XIAO-NAN LI","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIAO-NAN LI","raw_affiliation_strings":["Beihang University, Beijing 100191, P. R. China","Beihang University, Beijing, 100191, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]},{"raw_affiliation_string":"Beihang University, Beijing, 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023193123","display_name":"Guang-Mei Wei","orcid":"https://orcid.org/0000-0002-3111-7856","observed_orcids":["https://orcid.org/0000-0002-3111-7856"]},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"GUANG-MEI WEI","raw_affiliation_strings":["LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100191, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100673288","display_name":"Yuping Liu","orcid":"https://orcid.org/0000-0001-8053-0826","observed_orcids":["https://orcid.org/0000-0001-8053-0826"]},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YU-PING LIU","raw_affiliation_strings":["School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001635550","display_name":"Yueqian Liang","orcid":"https://orcid.org/0000-0003-0091-8789","observed_orcids":["https://orcid.org/0000-0003-0091-8789"]},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YUE-QIAN LIANG","raw_affiliation_strings":["LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100191, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMIB and School of Mathematics and System Sciences, Beihang University, Beijing 100191, P. R. China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022154543","display_name":"Xiang-Hua Meng","orcid":"https://orcid.org/0000-0002-2494-0916","observed_orcids":["https://orcid.org/0000-0002-2494-0916"]},"institutions":[{"id":"https://openalex.org/I78675632","display_name":"Beijing Information Science & Technology University","ror":"https://ror.org/04xnqep60","country_code":"CN","type":"education","lineage":["https://openalex.org/I78675632"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"XIANG-HUA MENG","raw_affiliation_strings":["Mathematics Department, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, P. R. China","institution_ids":["https://openalex.org/I78675632"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2191,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.56166995,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"28","issue":"14","first_page":"1450067","last_page":"1450067"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","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/1-1-dimensional-nonlinear-evolution-equations","display_name":"(1+1)-dimensional nonlinear evolution equations","score":0.8809999823570251},{"id":"https://openalex.org/keywords/painleve-test","display_name":"Painlev\u00e9 test","score":0.8870000243186951},{"id":"https://openalex.org/keywords/auto-backlund-transformation","display_name":"auto-B\u00e4cklund transformation","score":0.8560000061988831},{"id":"https://openalex.org/keywords/truncated-painleve-expansion","display_name":"truncated Painlev\u00e9 expansion","score":0.9330000281333923},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.6309999823570251},{"id":"https://openalex.org/keywords/periodic-solutions","display_name":"periodic solutions","score":0.7910000085830688},{"id":"https://openalex.org/keywords/soliton-like-solutions","display_name":"soliton-like solutions","score":0.9959999918937683},{"id":"https://openalex.org/keywords/similarity-reductions","display_name":"similarity reductions","score":0.9559999704360962},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"symbolic computation","score":0.6639999747276306}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8049411773681641},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.7752035856246948},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.7109984159469604},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.652729868888855},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5900739431381226},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5468182563781738},{"id":"https://openalex.org/C39739852","wikidata":"https://www.wikidata.org/wiki/Q254491","display_name":"Matrix similarity","level":3,"score":0.5193794369697571},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.5151270627975464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5138561725616455},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5107548236846924},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.44390174746513367},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.40858137607574463},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.39501065015792847},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3572825789451599},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3295663893222809},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32240599393844604},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2636716365814209},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2227683663368225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21857213973999023},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09820812940597534},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07295989990234375},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0217979214500672","doi":"https://doi.org/10.1142/s0217979214500672","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217979214500672","pdf_url":null,"source":{"id":"https://openalex.org/S130197424","display_name":"International Journal of Modern Physics B","issn_l":"0217-9792","issn":["0217-9792","1793-6578"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","jufo-1","norway-1"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modern Physics B","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":34,"referenced_works":["https://openalex.org/W595846807","https://openalex.org/W1972318738","https://openalex.org/W1972740435","https://openalex.org/W1979491229","https://openalex.org/W1983527430","https://openalex.org/W1985167223","https://openalex.org/W1989437483","https://openalex.org/W1993345032","https://openalex.org/W2000968358","https://openalex.org/W2001139209","https://openalex.org/W2009012105","https://openalex.org/W2009541255","https://openalex.org/W2029164146","https://openalex.org/W2029675429","https://openalex.org/W2031242006","https://openalex.org/W2035608176","https://openalex.org/W2048202664","https://openalex.org/W2057915046","https://openalex.org/W2064933276","https://openalex.org/W2066434432","https://openalex.org/W2072512350","https://openalex.org/W2079467227","https://openalex.org/W2083332431","https://openalex.org/W2083960709","https://openalex.org/W2084476741","https://openalex.org/W2084964440","https://openalex.org/W2086048908","https://openalex.org/W2089101801","https://openalex.org/W2094566231","https://openalex.org/W2099235198","https://openalex.org/W2119413556","https://openalex.org/W2565154731","https://openalex.org/W4232650420","https://openalex.org/W4242274835"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2996841952","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4288093367","https://openalex.org/W4382202915"],"abstract_inverted_index":{"The":[0,38],"(1+1)-dimensional":[1],"higher-order":[2],"Broer\u2013Kaup":[3],"(HBK)":[4],"system":[5,61],"is":[6,31],"investigated":[7],"in":[8],"this":[9],"paper.":[10],"Painlev\u00e9":[11,36],"test":[12],"shows":[13],"that":[14],"there":[15],"are":[16,42,62],"two":[17,66],"solution":[18],"branches,":[19],"one":[20],"of":[21,46],"which":[22],"has":[23],"the":[24,34,47,51,59],"resonance":[25],"-2.":[26],"And":[27],"an":[28],"auto-B\u00e4cklund":[29,48],"transformation":[30],"obtained":[32],"by":[33,44],"truncated":[35],"expansion.":[37],"new":[39],"analytic":[40],"solutions":[41],"presented":[43],"means":[45],"transformation,":[49],"including":[50],"periodic":[52],"and":[53],"soliton-like":[54],"solutions.":[55],"Similarity":[56],"reductions":[57],"for":[58],"HBK":[60],"given":[63],"out":[64],"to":[65],"ordinary":[67],"differential":[68],"equations":[69],"(ODEs)":[70],"through":[71],"CK":[72],"direct":[73],"method.":[74]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-09-27T08:07:27.782135","created_date":"2025-10-10T00:00:00"}