{"id":"https://openalex.org/W2135835065","doi":"https://doi.org/10.1155/s0161171204405456","title":"Multiplicity and structures for traveling wave solutions of the Kuramoto\u2010Sivashinsky equation","display_name":"Multiplicity and structures for traveling wave solutions of the Kuramoto\u2010Sivashinsky equation","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2135835065","doi":"https://doi.org/10.1155/s0161171204405456","mag":"2135835065"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171204405456","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204405456","pdf_url":null,"source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1155/s0161171204405456","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051244206","display_name":"Bao\u2010Feng Feng","orcid":"https://orcid.org/0000-0002-2529-897X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bao-Feng Feng","raw_affiliation_strings":["Department of Mathematics, The University of Texas \u2013 Pan American"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Texas \u2013 Pan American","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051244206"],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.20003849,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2004","issue":"70","first_page":"3839","last_page":"3848"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9889000058174133,"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/mathematics","display_name":"Mathematics","score":0.807117223739624},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.6741065979003906},{"id":"https://openalex.org/keywords/traveling-wave","display_name":"Traveling wave","score":0.6733598709106445},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6162490844726562},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5914038419723511},{"id":"https://openalex.org/keywords/shock-wave","display_name":"Shock wave","score":0.5760504007339478},{"id":"https://openalex.org/keywords/wavelength","display_name":"Wavelength","score":0.5207688212394714},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.48355790972709656},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.4638407826423645},{"id":"https://openalex.org/keywords/shock","display_name":"Shock (circulatory)","score":0.4372095465660095},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.24265891313552856},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19048744440078735},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.08995804190635681}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.807117223739624},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.6741065979003906},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.6733598709106445},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6162490844726562},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5914038419723511},{"id":"https://openalex.org/C70477161","wikidata":"https://www.wikidata.org/wiki/Q190688","display_name":"Shock wave","level":2,"score":0.5760504007339478},{"id":"https://openalex.org/C6260449","wikidata":"https://www.wikidata.org/wiki/Q41364","display_name":"Wavelength","level":2,"score":0.5207688212394714},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.48355790972709656},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4638407826423645},{"id":"https://openalex.org/C2781300812","wikidata":"https://www.wikidata.org/wiki/Q178061","display_name":"Shock (circulatory)","level":2,"score":0.4372095465660095},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24265891313552856},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19048744440078735},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.08995804190635681},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/s0161171204405456","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204405456","pdf_url":null,"source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:389587","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2004/389587.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:82b8cf852fe94b718271272dac211e30","is_oa":true,"landing_page_url":"https://doaj.org/article/82b8cf852fe94b718271272dac211e30","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2004, Iss 70, Pp 3839-3848 (2004)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/S0161171204405456","is_oa":false,"landing_page_url":"https://doi.org/10.1155/S0161171204405456","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.1155/s0161171204405456","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171204405456","pdf_url":null,"source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8399999737739563,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W111157985","https://openalex.org/W142640180","https://openalex.org/W1805381866","https://openalex.org/W1967198417","https://openalex.org/W1977255739","https://openalex.org/W1978470815","https://openalex.org/W1982999858","https://openalex.org/W2004204172","https://openalex.org/W2013615321","https://openalex.org/W2022491062","https://openalex.org/W2025647789","https://openalex.org/W2029792495","https://openalex.org/W2046527278","https://openalex.org/W2050973644","https://openalex.org/W2065378774","https://openalex.org/W2067139588","https://openalex.org/W2068246286","https://openalex.org/W2073061323","https://openalex.org/W2078887302","https://openalex.org/W2094925628","https://openalex.org/W2131567068","https://openalex.org/W2139886236","https://openalex.org/W2598306931","https://openalex.org/W3048551978","https://openalex.org/W4253294199"],"related_works":["https://openalex.org/W2347486132","https://openalex.org/W4230581126","https://openalex.org/W2350340797","https://openalex.org/W2052371115","https://openalex.org/W2079984045","https://openalex.org/W4293224283","https://openalex.org/W2316789606","https://openalex.org/W2950501077","https://openalex.org/W4378765297","https://openalex.org/W2368601041"],"abstract_inverted_index":{"The":[0],"Kuramoto\u2010Sivashinsky":[1],"(KS)":[2],"equation":[3,42],"is":[4,87,121],"known":[5],"as":[6],"a":[7,12,25,83],"popular":[8],"prototype":[9],"to":[10,89,97],"represent":[11],"system":[13],"in":[14,64],"which":[15],"the":[16,40,68,98,102,105,115],"transport":[17],"of":[18,54,61,70,77,101,108,118],"energy":[19],"through":[20],"nonlinear":[21],"mode":[22],"coupling":[23],"produces":[24],"balance":[26],"between":[27],"long":[28],"wavelength":[29,33],"instability":[30],"and":[31,51,59,114],"short":[32],"dissipation.":[34],"Existing":[35],"numerical":[36,78],"results":[37],"indicate":[38],"that":[39],"KS":[41],"admits":[43],"three":[44],"classes":[45],"(namely,":[46],"regular":[47,109],"shock,":[48,50],"oscillatory":[49],"solitary":[52],"wave)":[53],"nonperiodic":[55],"traveling":[56,93],"wave":[57,94],"solutions":[58,63,72],"families":[60,107],"multiple":[62,71,92],"each":[65,119],"class.":[66],"However,":[67],"details":[69],"are":[73,112],"still":[74],"unclear":[75],"because":[76],"accuracy.":[79],"In":[80],"this":[81],"work,":[82],"rational":[84],"spectral":[85],"approach":[86],"used":[88],"compute":[90],"these":[91],"solutions.":[95],"Owing":[96],"high":[99],"accuracy":[100],"employed":[103],"method,":[104],"new":[106],"shock":[110],"waves":[111],"found":[113],"fine":[116],"structure":[117],"family":[120],"recognized.":[122]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}