{"id":"https://openalex.org/W1994828676","doi":"https://doi.org/10.1142/s0218127407019858","title":"ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS","display_name":"ON A CLASS OF SINGULAR NONLINEAR TRAVELING WAVE EQUATIONS","publication_year":2007,"publication_date":"2007-11-01","ids":{"openalex":"https://openalex.org/W1994828676","doi":"https://doi.org/10.1142/s0218127407019858","mag":"1994828676"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127407019858","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019858","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":["Center for Nonlinear Science Studies, 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":"Center for Nonlinear Science Studies, 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/A5024633466","display_name":"Guanrong Chen","orcid":"https://orcid.org/0000-0003-1381-7418"},"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":"GUANRONG CHEN","raw_affiliation_strings":["Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7235,"has_fulltext":false,"cited_by_count":212,"citation_normalized_percentile":{"value":0.93645725,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"17","issue":"11","first_page":"4049","last_page":"4065"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9995999932289124,"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":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9986000061035156,"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/nonlinear-system","display_name":"Nonlinear system","score":0.675424337387085},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6589301228523254},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.6425755023956299},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6251630187034607},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6175526976585388},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5985021591186523},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5612075328826904},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.48535314202308655},{"id":"https://openalex.org/keywords/stokes-wave","display_name":"Stokes wave","score":0.46269187331199646},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4438777267932892},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4335230588912964},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3316904902458191},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.33143115043640137},{"id":"https://openalex.org/keywords/wave-propagation","display_name":"Wave propagation","score":0.2958177924156189},{"id":"https://openalex.org/keywords/breaking-wave","display_name":"Breaking wave","score":0.11793538928031921},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08659440279006958}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.675424337387085},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6589301228523254},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.6425755023956299},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6251630187034607},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6175526976585388},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5985021591186523},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5612075328826904},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.48535314202308655},{"id":"https://openalex.org/C53630964","wikidata":"https://www.wikidata.org/wiki/Q7618554","display_name":"Stokes wave","level":4,"score":0.46269187331199646},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4438777267932892},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4335230588912964},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3316904902458191},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.33143115043640137},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.2958177924156189},{"id":"https://openalex.org/C169596890","wikidata":"https://www.wikidata.org/wiki/Q661247","display_name":"Breaking wave","level":3,"score":0.11793538928031921},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08659440279006958},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127407019858","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127407019858","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1491439616","https://openalex.org/W1603340857","https://openalex.org/W1604213221","https://openalex.org/W1969711311","https://openalex.org/W1970680427","https://openalex.org/W1984628902","https://openalex.org/W1990720130","https://openalex.org/W1996488036","https://openalex.org/W2031267663","https://openalex.org/W2033734904","https://openalex.org/W2070077167","https://openalex.org/W2080887215","https://openalex.org/W2084424709","https://openalex.org/W2087646556","https://openalex.org/W2089876099","https://openalex.org/W2323070876","https://openalex.org/W4250716583","https://openalex.org/W4252247111","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W1997022868","https://openalex.org/W2061818987","https://openalex.org/W2058973986","https://openalex.org/W4287780914","https://openalex.org/W3034862729","https://openalex.org/W3023599262","https://openalex.org/W2064520184","https://openalex.org/W1970842439","https://openalex.org/W2706310289","https://openalex.org/W2054370674"],"abstract_inverted_index":{"The":[0],"existence":[1,63],"of":[2,11,14,33,39,41,50,64],"solitary":[3],"wave,":[4],"kink":[5],"wave":[6,9,35,43,53],"and":[7,70],"periodic":[8],"solutions":[10,44,67],"a":[12,31],"class":[13,32],"singular":[15],"reaction\u2013diffusion":[16],"equations":[17],"is":[18],"obtained":[19],"using":[20],"some":[21,47],"effective":[22],"methods":[23],"from":[24],"the":[25,51,62,65],"dynamical":[26],"systems":[27,54],"theory.":[28],"Specially,":[29],"for":[30],"nonlinear":[34],"equations,":[36],"fundamental":[37],"properties":[38],"profiles":[40],"traveling":[42,52],"determined":[45],"by":[46],"bounded":[48],"orbits":[49],"are":[55,68],"rigorously":[56],"proved.":[57],"Parametric":[58],"conditions":[59],"that":[60],"guarantee":[61],"aforementioned":[66],"derived":[69],"given":[71],"explicitly.":[72]},"counts_by_year":[{"year":2026,"cited_by_count":15},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":18},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":4}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
