{"id":"https://openalex.org/W2477435071","doi":"https://doi.org/10.1142/s0218127416501364","title":"Exact Solutions and Bifurcations in Invariant Manifolds for a Nonic Derivative Nonlinear Schr\u00f6dinger Equation","display_name":"Exact Solutions and Bifurcations in Invariant Manifolds for a Nonic Derivative Nonlinear Schr\u00f6dinger Equation","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2477435071","doi":"https://doi.org/10.1142/s0218127416501364","mag":"2477435071"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127416501364","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501364","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/I119045251","display_name":"Huaqiao University","ror":"https://ror.org/03frdh605","country_code":"CN","type":"education","lineage":["https://openalex.org/I119045251"]},{"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":true,"raw_author_name":"Jibin Li","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, 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":"School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100599691"],"corresponding_institution_ids":["https://openalex.org/I119045251","https://openalex.org/I135237710"],"apc_list":null,"apc_paid":null,"fwci":0.4297,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65171885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"26","issue":"08","first_page":"1650136","last_page":"1650136"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9990000128746033,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9990000128746033,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9988999962806702,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.995199978351593,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/phase-portrait","display_name":"Phase portrait","score":0.8164196610450745},{"id":"https://openalex.org/keywords/homoclinic-orbit","display_name":"Homoclinic orbit","score":0.7337947487831116},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.7122577428817749},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.65957111120224},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6208286285400391},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5662574768066406},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5603854060173035},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5465540289878845},{"id":"https://openalex.org/keywords/invariant-manifold","display_name":"Invariant manifold","score":0.5029067397117615},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4301265478134155},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.39266565442085266},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.3533456325531006},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1845119297504425},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09439072012901306}],"concepts":[{"id":"https://openalex.org/C122283620","wikidata":"https://www.wikidata.org/wiki/Q2532943","display_name":"Phase portrait","level":4,"score":0.8164196610450745},{"id":"https://openalex.org/C200581526","wikidata":"https://www.wikidata.org/wiki/Q690494","display_name":"Homoclinic orbit","level":4,"score":0.7337947487831116},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7122577428817749},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.65957111120224},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6208286285400391},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5662574768066406},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5603854060173035},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5465540289878845},{"id":"https://openalex.org/C20483540","wikidata":"https://www.wikidata.org/wiki/Q4200516","display_name":"Invariant manifold","level":2,"score":0.5029067397117615},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4301265478134155},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.39266565442085266},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.3533456325531006},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1845119297504425},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09439072012901306},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127416501364","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127416501364","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":8,"referenced_works":["https://openalex.org/W1975443095","https://openalex.org/W1994828676","https://openalex.org/W2021260349","https://openalex.org/W2038735336","https://openalex.org/W2062265971","https://openalex.org/W2078134231","https://openalex.org/W2089876099","https://openalex.org/W4289981527"],"related_works":["https://openalex.org/W1536954903","https://openalex.org/W2971857410","https://openalex.org/W4288115441","https://openalex.org/W4313501365","https://openalex.org/W2043393553","https://openalex.org/W2129195111","https://openalex.org/W1972846926","https://openalex.org/W2006002535","https://openalex.org/W3049020700","https://openalex.org/W2118916106"],"abstract_inverted_index":{"Propagating":[0],"modes":[1],"in":[2,33,71],"a":[3,43,56],"class":[4],"of":[5,20,54,75,85,93,134],"nonic":[6],"derivative":[7],"nonlinear":[8],"Schr\u00f6dinger":[9],"equations":[10],"incorporating":[11],"ninth":[12],"order":[13],"nonlinearity":[14],"are":[15,136],"investigated":[16],"by":[17],"the":[18,24,34,52,61,72,76,82],"method":[19],"dynamical":[21,58,86,107],"systems.":[22],"Because":[23],"functions":[25],"[Formula:":[26,30,36,39,65,118,122],"see":[27,31,37,40,66,119,123],"text]":[28,32,41,67,120,124],"and":[29,96,101,121],"solutions":[35,103,117,133],"text],":[38],"satisfy":[42],"four-dimensional":[44,77],"integral":[45],"system":[46,59,108],"having":[47],"two":[48],"first":[49],"integrals":[50],"(i.e.":[51],"invariants":[53],"motion),":[55],"planar":[57,106],"for":[60,104],"squared":[62],"wave":[63],"amplitude":[64],"can":[68,109,125],"be":[69,110,126],"derived":[70],"invariant":[73],"manifold":[74],"integrable":[78],"system.":[79],"By":[80],"using":[81],"bifurcation":[83],"theory":[84],"systems,":[87],"under":[88,113],"different":[89],"parameter":[90,115],"conditions,":[91,116],"bifurcations":[92],"phase":[94],"portraits":[95],"exact":[97,131],"periodic":[98],"solutions,":[99],"homoclinic":[100],"heteroclinic":[102],"this":[105],"given.":[111],"Therefore,":[112],"some":[114],"exactly":[127],"obtained.":[128],"Thirty":[129],"six":[130],"explicit":[132],"equation":[135],"derived.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}