{"id":"https://openalex.org/W2018603946","doi":"https://doi.org/10.1142/s0218127411028581","title":"HOMOCLINIC MANIFOLDS, CENTER MANIFOLDS AND EXACT SOLUTIONS OF FOUR-DIMENSIONAL TRAVELING WAVE SYSTEMS FOR TWO CLASSES OF NONLINEAR WAVE EQUATIONS","display_name":"HOMOCLINIC MANIFOLDS, CENTER MANIFOLDS AND EXACT SOLUTIONS OF FOUR-DIMENSIONAL TRAVELING WAVE SYSTEMS FOR TWO CLASSES OF NONLINEAR WAVE EQUATIONS","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W2018603946","doi":"https://doi.org/10.1142/s0218127411028581","mag":"2018603946"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127411028581","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028581","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Bifurcation and Chaos","raw_type":"journal-article"},"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/A5100599691","display_name":"Jibin Li","orcid":"https://orcid.org/0000-0003-4839-5956"},"institutions":[{"id":"https://openalex.org/I10660446","display_name":"Kunming University of Science and Technology","ror":"https://ror.org/00xyeez13","country_code":"CN","type":"education","lineage":["https://openalex.org/I10660446"]},{"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"JIBIN LI","raw_affiliation_strings":["Department of Mathematics, Kunming University of Science, and Technology, Kunming, Yunnan 650093, P. R. China","Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Kunming University of Science, and Technology, Kunming, Yunnan 650093, P. R. China","institution_ids":["https://openalex.org/I10660446"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100661899","display_name":"Yi Zhang","orcid":"https://orcid.org/0000-0001-7764-4953"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YI ZHANG","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P. R. China","institution_ids":["https://openalex.org/I135237710"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2356,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.55464899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"02","first_page":"527","last_page":"543"},"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":0.9994000196456909,"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":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.9698124527931213},{"id":"https://openalex.org/keywords/center-manifold","display_name":"Center manifold","score":0.683262825012207},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6071969866752625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5912720561027527},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.5801483392715454},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5796641707420349},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.56169593334198},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.5564880967140198},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5408755540847778},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5237514972686768},{"id":"https://openalex.org/keywords/stable-manifold","display_name":"Stable manifold","score":0.4811374247074127},{"id":"https://openalex.org/keywords/homoclinic-bifurcation","display_name":"Homoclinic bifurcation","score":0.4759092926979065},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4697414040565491},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.46456682682037354},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2911762595176697},{"id":"https://openalex.org/keywords/hopf-bifurcation","display_name":"Hopf bifurcation","score":0.17802554368972778}],"concepts":[{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.9698124527931213},{"id":"https://openalex.org/C74774103","wikidata":"https://www.wikidata.org/wiki/Q4504202","display_name":"Center manifold","level":5,"score":0.683262825012207},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6071969866752625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5912720561027527},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.5801483392715454},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5796641707420349},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.56169593334198},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.5564880967140198},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5408755540847778},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5237514972686768},{"id":"https://openalex.org/C50429861","wikidata":"https://www.wikidata.org/wiki/Q3554830","display_name":"Stable manifold","level":2,"score":0.4811374247074127},{"id":"https://openalex.org/C155405617","wikidata":"https://www.wikidata.org/wiki/Q1154357","display_name":"Homoclinic bifurcation","level":5,"score":0.4759092926979065},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4697414040565491},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.46456682682037354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2911762595176697},{"id":"https://openalex.org/C172435161","wikidata":"https://www.wikidata.org/wiki/Q531126","display_name":"Hopf bifurcation","level":4,"score":0.17802554368972778},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127411028581","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127411028581","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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 Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1966470051","https://openalex.org/W2013778694","https://openalex.org/W2038095811","https://openalex.org/W2046323608","https://openalex.org/W2050870564","https://openalex.org/W2053313687","https://openalex.org/W2080199241","https://openalex.org/W2080513292","https://openalex.org/W2089996117","https://openalex.org/W2094534254","https://openalex.org/W2127023136","https://openalex.org/W2166499524","https://openalex.org/W3038085088","https://openalex.org/W3104252319","https://openalex.org/W4244751682"],"related_works":["https://openalex.org/W2592370375","https://openalex.org/W1547807244","https://openalex.org/W2358211602","https://openalex.org/W2353823404","https://openalex.org/W2096695703","https://openalex.org/W2129195111","https://openalex.org/W2061154922","https://openalex.org/W2018447484","https://openalex.org/W2063858073","https://openalex.org/W2000817226"],"abstract_inverted_index":{"For":[0],"the":[1,6],"Lax":[2],"KdV5":[3],"equation":[4],"and":[5,28,50],"KdV\u2013Sawada\u2013Kotera\u2013Ramani":[7],"equation,":[8],"their":[9],"corresponding":[10],"four-dimensional":[11],"traveling":[12],"wave":[13,30],"systems":[14],"are":[15,32,65],"studied":[16],"by":[17],"using":[18],"Congrove's":[19],"method.":[20],"Exact":[21],"explicit":[22],"gap":[23],"soliton,":[24,26],"embedded":[25],"periodic":[27],"quasi-periodic":[29],"solutions":[31],"obtained.":[33],"The":[34,60],"existence":[35],"of":[36,42,56,63],"homoclinic":[37],"manifolds":[38],"to":[39],"three":[40],"kinds":[41],"equilibria":[43,64],"including":[44],"a":[45,48],"hyperbolic":[46],"equilibrium,":[47],"center-saddle":[49],"an":[51],"equilibrium":[52],"with":[53],"zero":[54],"pair":[55],"eigenvalues":[57],"is":[58],"revealed.":[59],"bifurcation":[61],"conditions":[62],"given.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
