{"id":"https://openalex.org/W4415620685","doi":"https://doi.org/10.1142/s0218127425400103","title":"Finding and Analyzing the Solutions of Singular Nonlinear Traveling Wave Equations: A Dynamical Systems Approach","display_name":"Finding and Analyzing the Solutions of Singular Nonlinear Traveling Wave Equations: A Dynamical Systems Approach","publication_year":2025,"publication_date":"2025-10-25","ids":{"openalex":"https://openalex.org/W4415620685","doi":"https://doi.org/10.1142/s0218127425400103"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127425400103","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425400103","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":false,"raw_author_name":"Jibin Li","raw_affiliation_strings":["Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China","School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-4839-5956","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 Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]},{"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 Electrical Engineering, City University of Hong Kong, Hong Kong 999077, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-1381-7418","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, City University of Hong Kong, Hong Kong 999077, 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":2.0371,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87673508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"35","issue":"14","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":0.8863999843597412,"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":0.8863999843597412,"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":0.04839999973773956,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.01899999938905239,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/peakon","display_name":"Peakon","score":0.9728000164031982},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7484999895095825},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.6747000217437744},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6685000061988831},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6366000175476074},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5425999760627747},{"id":"https://openalex.org/keywords/periodic-wave","display_name":"Periodic wave","score":0.48730000853538513}],"concepts":[{"id":"https://openalex.org/C155091195","wikidata":"https://www.wikidata.org/wiki/Q7157892","display_name":"Peakon","level":3,"score":0.9728000164031982},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7484999895095825},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.6747000217437744},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6685000061988831},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6366000175476074},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5583999752998352},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5425999760627747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5274999737739563},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.48730000853538513},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4706999957561493},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.461899995803833},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.39149999618530273},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C93812963","wikidata":"https://www.wikidata.org/wiki/Q7249433","display_name":"Projected dynamical system","level":5,"score":0.3131999969482422},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.30300000309944153},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127425400103","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127425400103","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":[{"id":"https://openalex.org/G2252944680","display_name":null,"funder_award_id":"11701191","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4979587629","display_name":null,"funder_award_id":"1201530062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G579299895","display_name":"\u4e0d\u8fde\u7eed\u6cdb\u51fd\u5fae\u5206\u65b9\u7a0b\u52a8\u529b\u5b66\u884c\u4e3a\u4e0e\u63a7\u5236\u7814\u7a76","funder_award_id":"11871231","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6199456687","display_name":"\u6d45\u6c34\u6ce2\u65b9\u7a0b\u7684\u884c\u6ce2\u89e3\u7814\u7a76\uff1a\u52a8\u529b\u7cfb\u7edf\u65b9\u6cd5\u548c\u51e0\u4f55\u5947\u5f02\u6444\u52a8\u7406\u8bba","funder_award_id":"12071162","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7183490805","display_name":"\u51e0\u7c7b\u9ad8\u9636\u975e\u7ebf\u6027\u884c\u6ce2\u65b9\u7a0b\u7684\u7cbe\u786e\u89e3,\u5206\u652f\u548c\u590d\u6742\u52a8\u529b\u5b66\u7814\u7a76","funder_award_id":"11471289","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7818855132","display_name":"\u5947\u6ce2\u548c\u602a\u6ce2\u6a21\u578b\u7684\u52a8\u529b\u5b66\u6027\u8d28\u7814\u7a76","funder_award_id":"11571318","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G824913788","display_name":"\u975e\u7ebf\u6027\u6ce2\u6a21\u578b\u8026\u5408\u96c6\u6210\u7684\u52a8\u529b\u5b66\u7814\u7a76","funder_award_id":"11162020","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":false,"pdf":false},"content_urls":null,"referenced_works_count":76,"referenced_works":["https://openalex.org/W1887903210","https://openalex.org/W1970261423","https://openalex.org/W1980255316","https://openalex.org/W1989102406","https://openalex.org/W1990416478","https://openalex.org/W1992384758","https://openalex.org/W1994828676","https://openalex.org/W1997469526","https://openalex.org/W1998311152","https://openalex.org/W2003499712","https://openalex.org/W2007453416","https://openalex.org/W2008556889","https://openalex.org/W2009961065","https://openalex.org/W2012844428","https://openalex.org/W2017182685","https://openalex.org/W2018603946","https://openalex.org/W2020430873","https://openalex.org/W2023684980","https://openalex.org/W2029328754","https://openalex.org/W2031131626","https://openalex.org/W2032753438","https://openalex.org/W2038735336","https://openalex.org/W2040086930","https://openalex.org/W2041891623","https://openalex.org/W2046881861","https://openalex.org/W2047072153","https://openalex.org/W2048106217","https://openalex.org/W2052528969","https://openalex.org/W2067903388","https://openalex.org/W2071969012","https://openalex.org/W2076383796","https://openalex.org/W2079127676","https://openalex.org/W2080887215","https://openalex.org/W2081735292","https://openalex.org/W2091234113","https://openalex.org/W2108202098","https://openalex.org/W2116250046","https://openalex.org/W2140084231","https://openalex.org/W2156646326","https://openalex.org/W2167702145","https://openalex.org/W2169817014","https://openalex.org/W2178918010","https://openalex.org/W2205469801","https://openalex.org/W2234746416","https://openalex.org/W2294957588","https://openalex.org/W2323070876","https://openalex.org/W2327440264","https://openalex.org/W2552776555","https://openalex.org/W2606722229","https://openalex.org/W2738147973","https://openalex.org/W2774493344","https://openalex.org/W2776321568","https://openalex.org/W2791946743","https://openalex.org/W2912449497","https://openalex.org/W2944374394","https://openalex.org/W2956165046","https://openalex.org/W2964333265","https://openalex.org/W2990848478","https://openalex.org/W3005602031","https://openalex.org/W3014509752","https://openalex.org/W3040454514","https://openalex.org/W3042587952","https://openalex.org/W3048119777","https://openalex.org/W3125559884","https://openalex.org/W3146426965","https://openalex.org/W3216647273","https://openalex.org/W4224864068","https://openalex.org/W4289981527","https://openalex.org/W4320017736","https://openalex.org/W4388788260","https://openalex.org/W4392302625","https://openalex.org/W4404395737","https://openalex.org/W4405870537","https://openalex.org/W4410132710","https://openalex.org/W4410857880","https://openalex.org/W7077674152"],"related_works":[],"abstract_inverted_index":{"This":[0],"overview":[1],"paper":[2],"reviews":[3],"a":[4,78,82,88,92,199],"dynamical":[5,48],"systems":[6,49,171,176],"approach":[7],"to":[8,123,164,192],"studying":[9],"the":[10,17,31,37,45,51,58,64,67,101,137,142,147,151,178],"singular":[11,54,173],"nonlinear":[12,117,202],"traveling":[13,55,169,174],"wave":[14,56,118,170,175],"equations.":[15],"First,":[16],"notion":[18],"of":[19,47,53,63,66,81,84,91,94,177,201,204],"exact":[20,59,129],"peakon,":[21,23],"periodic":[22,85],"pseudo-peakon,":[24],"as":[25,27],"well":[26],"compacton":[28],"solutions":[29,65,73,110],"for":[30],"generalized":[32,143],"Camassa\u2013Holm":[33],"(CH)":[34],"equation":[35,119,145],"and":[36,50,103,146,196],"Degasperis\u2013Procesi":[38],"(DP)":[39],"equation,":[40],"is":[41,77,190],"introduced.":[42],"Based":[43],"on":[44],"method":[46],"theory":[52,195],"equations,":[57],"explicit":[60,130],"parametric":[61],"representations":[62],"above-mentioned":[68],"equations":[69],"are":[70,107,121,134,172],"derived.":[71],"These":[72],"show":[74,124],"that":[75,125],"peakon":[76,105,131,138,184],"limit":[79,89,98],"solution":[80,90,139],"family":[83,93],"peakons":[86],"or":[87],"pseudo-peakons":[95],"in":[96,111,156],"different":[97,113,135],"senses,":[99],"whereas":[100],"pseudo-peakon":[102],"pseudo-periodic":[104],"families":[106],"smooth":[108],"classical":[109],"two":[112],"time":[114],"scales.":[115],"Second,":[116],"models":[120],"introduced":[122],"there":[126],"exist":[127],"various":[128],"solutions,":[132],"which":[133,181],"from":[136],"given":[140],"by":[141],"CH":[144],"DP":[148],"equation.":[149],"Third,":[150],"so-called":[152],"\u201cpeakon":[153,166],"equations\u201d":[154],"discussed":[155],"some":[157],"studies":[158],"actually":[159],"have":[160,183],"no":[161],"peakons.":[162],"Corresponding":[163],"these":[165],"equations\u201d,":[167],"their":[168],"second":[179],"kind,":[180],"cannot":[182],"solutions.":[185],"Finally,":[186],"an":[187],"application":[188],"example":[189],"presented":[191],"illustrate":[193],"our":[194],"methodology":[197],"using":[198],"model":[200],"elastodynamics":[203],"materials":[205],"with":[206],"strong":[207],"ellipticity.":[208]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-28T00:00:00"}
