{"id":"https://openalex.org/W2990848478","doi":"https://doi.org/10.1142/s0218127419501530","title":"Exact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave Equations","display_name":"Exact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave Equations","publication_year":2019,"publication_date":"2019-11-01","ids":{"openalex":"https://openalex.org/W2990848478","doi":"https://doi.org/10.1142/s0218127419501530","mag":"2990848478"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127419501530","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501530","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 Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"],"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":"middle","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 SAR, P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014101119","display_name":"Jie Song","orcid":"https://orcid.org/0000-0002-2243-3902"},"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"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Song","raw_affiliation_strings":["School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Huaqiao University, Quanzhou, Fujian 362021, P. R. China","institution_ids":["https://openalex.org/I119045251"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":0.4344,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62261707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"29","issue":"12","first_page":"1950153","last_page":"1950153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9961000084877014,"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/T11061","display_name":"Ocean Waves and Remote Sensing","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/peakon","display_name":"Peakon","score":0.9870057702064514},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5290499925613403},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5179111361503601},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.504219651222229},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.49221673607826233},{"id":"https://openalex.org/keywords/periodic-wave","display_name":"Periodic wave","score":0.44604766368865967},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.44114840030670166},{"id":"https://openalex.org/keywords/waves-and-shallow-water","display_name":"Waves and shallow water","score":0.4299498200416565},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.38935038447380066},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.31931596994400024},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07647991180419922},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.06313890218734741}],"concepts":[{"id":"https://openalex.org/C155091195","wikidata":"https://www.wikidata.org/wiki/Q7157892","display_name":"Peakon","level":3,"score":0.9870057702064514},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5290499925613403},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5179111361503601},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.504219651222229},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.49221673607826233},{"id":"https://openalex.org/C2993172089","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Periodic wave","level":3,"score":0.44604766368865967},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.44114840030670166},{"id":"https://openalex.org/C186348155","wikidata":"https://www.wikidata.org/wiki/Q7975538","display_name":"Waves and shallow water","level":2,"score":0.4299498200416565},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.38935038447380066},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.31931596994400024},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07647991180419922},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.06313890218734741},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/s0218127419501530","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127419501530","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":[{"id":"https://metadata.un.org/sdg/6","display_name":"Clean water and sanitation","score":0.75}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1592624489","https://openalex.org/W1887903210","https://openalex.org/W1974313981","https://openalex.org/W1994828676","https://openalex.org/W1998646770","https://openalex.org/W2003499712","https://openalex.org/W2026031976","https://openalex.org/W2027877464","https://openalex.org/W2041891623","https://openalex.org/W2047072153","https://openalex.org/W2065465605","https://openalex.org/W2081935308","https://openalex.org/W2108202098","https://openalex.org/W2116250046","https://openalex.org/W2141317782","https://openalex.org/W2148003806","https://openalex.org/W2178918010","https://openalex.org/W2552776555","https://openalex.org/W4245261017","https://openalex.org/W4289981527"],"related_works":["https://openalex.org/W4224864068","https://openalex.org/W1965864985","https://openalex.org/W3019927421","https://openalex.org/W4308430545","https://openalex.org/W2509546410","https://openalex.org/W2277269733","https://openalex.org/W2006854657","https://openalex.org/W4286504938","https://openalex.org/W4386425857","https://openalex.org/W3143453476"],"abstract_inverted_index":{"Using":[0],"the":[1,17,34,76,101,106,109],"dynamical":[2],"systems":[3],"analysis":[4],"and":[5,13,19,49,63,88],"singular":[6],"traveling":[7],"wave":[8,24,42,45,86],"theory":[9],"developed":[10],"by":[11],"Li":[12],"Chen":[14],"[2007]":[15],"to":[16],"classical":[18],"modified":[20,77,110],"Serre":[21,78,111],"shallow":[22],"water":[23],"equations,":[25],"it":[26,95],"is":[27,71,96],"shown":[28],"that,":[29,73,98],"in":[30],"different":[31],"regions":[32],"of":[33,105,117],"parameter":[35],"space,":[36],"all":[37],"possible":[38],"bounded":[39],"solutions":[40,87],"(solitary":[41],"solutions,":[43,46],"kink":[44],"peakons,":[47],"pseudo-peakons":[48],"periodic":[50],"peakons":[51],"as":[52,54],"well":[53],"compactons)":[55],"can":[56],"be":[57],"obtained.":[58],"More":[59],"than":[60],"28":[61],"explicit":[62],"exact":[64],"parametric":[65],"representations":[66],"are":[67],"precisely":[68],"derived.":[69],"It":[70],"demonstrated":[72],"more":[74],"interestingly,":[75],"equation":[79,112],"has":[80,113],"uncountably":[81,89],"infinitely":[82,90],"many":[83,91],"smooth":[84],"solitary":[85],"pseudo-peakon":[92],"solutions.":[93,119],"Moreover,":[94],"found":[97],"differing":[99],"from":[100],"well-known":[102],"peakon":[103,118],"solution":[104],"Camassa\u2013Holm":[107],"equation,":[108],"four":[114],"new":[115],"forms":[116]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
