{"id":"https://openalex.org/W2070669548","doi":"https://doi.org/10.1155/2007/52020","title":"Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation","display_name":"Existence and Orbital Stability of Cnoidal Waves for a 1D Boussinesq Equation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2070669548","doi":"https://doi.org/10.1155/2007/52020","mag":"2070669548"},"language":"lv","primary_location":{"id":"doi:10.1155/2007/52020","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/52020","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/052020.pdf","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://downloads.hindawi.com/journals/ijmms/2007/052020.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000195982","display_name":"Jaime Angulo Pava","orcid":"https://orcid.org/0000-0002-7453-1782"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]},{"id":"https://openalex.org/I4210131883","display_name":"Brazilian Society of Computational and Applied Mathematics","ror":"https://ror.org/03kcw4w74","country_code":"BR","type":"other","lineage":["https://openalex.org/I4210131883"]},{"id":"https://openalex.org/I91732220","display_name":"Universidad del Valle","ror":"https://ror.org/00jb9vg53","country_code":"CO","type":"education","lineage":["https://openalex.org/I91732220"]}],"countries":["BR","CO"],"is_corresponding":false,"raw_author_name":"Jaime Angulo","raw_affiliation_strings":["Departamento de Matem\u00e1tica, Instituto de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e4o Cient\u00edfica, (IMECC), UNICAMP, CP 6065, Campinas, S\u00e4o Paulo CEP 13083-970","University of Valle"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1tica, Instituto de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e4o Cient\u00edfica, (IMECC), UNICAMP, CP 6065, Campinas, S\u00e4o Paulo CEP 13083-970","institution_ids":["https://openalex.org/I4210131883","https://openalex.org/I181391015"]},{"raw_affiliation_string":"University of Valle","institution_ids":["https://openalex.org/I91732220"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071443362","display_name":"Jos\u00e9 R. Quintero","orcid":"https://orcid.org/0000-0002-8762-3598"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]},{"id":"https://openalex.org/I4210122576","display_name":"Universidad del Valle","ror":"https://ror.org/02xw8cw23","country_code":"CR","type":"education","lineage":["https://openalex.org/I4210122576"]}],"countries":["BR","CR"],"is_corresponding":false,"raw_author_name":"Jose R. Quintero","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Universidad del Valle, Cali A. A. 25360","State University of Campinas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Universidad del Valle, Cali A. A. 25360","institution_ids":["https://openalex.org/I4210122576"]},{"raw_affiliation_string":"State University of Campinas","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":1.3086,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.77721857,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2007","issue":null,"first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9954000115394592,"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":0.9865999817848206,"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/algorithm","display_name":"Algorithm","score":0.3584776222705841},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17785438895225525}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3584776222705841},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17785438895225525}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2007/52020","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/52020","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/052020.pdf","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:052020","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2007/052020.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:ff414ac62c7c4a8c80168c4609b79fc1","is_oa":true,"landing_page_url":"https://doaj.org/article/ff414ac62c7c4a8c80168c4609b79fc1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 2007 (2007)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2007/52020","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2007/52020","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2007/052020.pdf","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":[],"awards":[{"id":"https://openalex.org/G2567251097","display_name":null,"funder_award_id":"300654/96-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G3027035349","display_name":null,"funder_award_id":"300654/96-0","funder_id":"https://openalex.org/F4320324328","funder_display_name":"Universidad del Valle"},{"id":"https://openalex.org/G3451381341","display_name":null,"funder_award_id":"2005/56331-9","funder_id":"https://openalex.org/F4320324328","funder_display_name":"Universidad del Valle"},{"id":"https://openalex.org/G353928835","display_name":null,"funder_award_id":"1106-05-16858","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G3677729678","display_name":null,"funder_award_id":"2005/56331-9","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G4944415858","display_name":null,"funder_award_id":"300654/96-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G5274807396","display_name":null,"funder_award_id":"1106-05-16858","funder_id":"https://openalex.org/F4320324328","funder_display_name":"Universidad del Valle"},{"id":"https://openalex.org/G759675390","display_name":null,"funder_award_id":"2005/56331-9","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8289540792","display_name":null,"funder_award_id":"1106-05-16858","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320309955","display_name":"Departamento Administrativo de Ciencia, Tecnolog\u00eda e Innovaci\u00f3n (COLCIENCIAS)","ror":"https://ror.org/048jthh02"},{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320323854","display_name":"Universidade Estadual de Campinas","ror":"https://ror.org/04wffgt70"},{"id":"https://openalex.org/F4320324328","display_name":"Universidad del Valle","ror":"https://ror.org/00jb9vg53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2070669548.pdf","grobid_xml":"https://content.openalex.org/works/W2070669548.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W84922499","https://openalex.org/W1527296550","https://openalex.org/W1771769068","https://openalex.org/W1966652217","https://openalex.org/W1979722387","https://openalex.org/W2006365463","https://openalex.org/W2061411896","https://openalex.org/W2103667682","https://openalex.org/W2133914554","https://openalex.org/W2155566813","https://openalex.org/W2209000373","https://openalex.org/W2279412724","https://openalex.org/W2497554230","https://openalex.org/W2596004680","https://openalex.org/W3193367371","https://openalex.org/W4213132260"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"We":[0],"will":[1],"study":[2,67],"the":[3,12,52,69,75],"existence":[4],"and":[5,62],"stability":[6,54],"of":[7,11,38,51,68],"periodic":[8,42,70],"travelling-wave":[9,20],"solutions":[10,21,40],"nonlinear":[13],"one-dimensional":[14],"Boussinesq-type":[15],"equation<mml:math":[16],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,27,46],"id=\"E1\"><mml:mrow><mml:msub><mml:mi>\u03a6</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>\u2212</mml:mo><mml:msub><mml:mi>\u03a6</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mi>a</mml:mi><mml:msub><mml:mi>\u03a6</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>\u2212</mml:mo><mml:mi>b</mml:mi><mml:msub><mml:mi>\u03a6</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi><mml:mi>t</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>\u03a6</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:msub><mml:mi>\u03a6</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>\u03a6</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:msub><mml:mi>\u03a6</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>.":[18],"Periodic":[19],"with":[22,44],"an":[23],"arbitrary":[24],"fundamental":[25],"period<mml:math":[26,45],"id=\"E2\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math>will":[28],"be":[29,48],"built":[30],"by":[31,41,57],"using":[32],"Jacobian":[33],"elliptic":[34],"functions.":[35],"Stability":[36],"(orbital)":[37],"these":[39],"disturbances":[43],"id=\"E3\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow></mml:math>will":[47],"a":[49],"consequence":[50],"general":[53],"criteria":[55],"given":[56],"M.":[58],"Grillakis,":[59],"J.":[60],"Shatah,":[61],"W.":[63],"Strauss.":[64],"A":[65],"complete":[66],"eigenvalue":[71],"problem":[72],"associated":[73],"to":[74],"Lame":[76],"equation":[77],"is":[78],"set":[79],"up.":[80]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}