{"id":"https://openalex.org/W2961908618","doi":"https://doi.org/10.15446/recolma.v53n1.81045","title":"Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber","display_name":"Existence of periodic standing wave solutions for a system describing pulse propagation in an optical fiber","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2961908618","doi":"https://doi.org/10.15446/recolma.v53n1.81045","mag":"2961908618"},"language":"en","primary_location":{"id":"doi:10.15446/recolma.v53n1.81045","doi":"https://doi.org/10.15446/recolma.v53n1.81045","is_oa":true,"landing_page_url":"https://doi.org/10.15446/recolma.v53n1.81045","pdf_url":null,"source":{"id":"https://openalex.org/S4210171540","display_name":"Revista Colombiana de Matem\u00e1ticas","issn_l":"0034-7426","issn":["0034-7426","2357-4100"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","publindex-c","russia-white-list-4"],"host_organization":"https://openalex.org/P4310318911","host_organization_name":"National University of Colombia","host_organization_lineage":["https://openalex.org/P4310318911"],"host_organization_lineage_names":["National University of Colombia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Colombiana de Matem\u00e1ticas","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.15446/recolma.v53n1.81045","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005278372","display_name":"Felipe Alexander Pipicano","orcid":"https://orcid.org/0000-0002-4983-9531","observed_orcids":["https://orcid.org/0000-0002-4983-9531"]},"institutions":[{"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"]},{"id":"https://openalex.org/I4210127437","display_name":"Universidad del Valle","ror":"https://ror.org/034me3y30","country_code":"NI","type":"education","lineage":["https://openalex.org/I4210127437"]},{"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":["CO","CR","NI"],"is_corresponding":false,"raw_author_name":"Felipe Alexander Pipicano","raw_affiliation_strings":["Universidad del Valle - Facultad de Ciencias - Departamento de Matem\u00e1ticas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad del Valle - Facultad de Ciencias - Departamento de Matem\u00e1ticas","institution_ids":["https://openalex.org/I4210122576","https://openalex.org/I4210127437","https://openalex.org/I91732220"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065812512","display_name":"Juan Carlos Mu\u00f1oz Grajales","orcid":"https://orcid.org/0000-0002-6824-1957","observed_orcids":["https://orcid.org/0000-0002-6824-1957"]},"institutions":[{"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"]},{"id":"https://openalex.org/I4210127437","display_name":"Universidad del Valle","ror":"https://ror.org/034me3y30","country_code":"NI","type":"education","lineage":["https://openalex.org/I4210127437"]},{"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":["CO","CR","NI"],"is_corresponding":false,"raw_author_name":"Juan Carlos Mu\u00f1oz Grajales","raw_affiliation_strings":["Universidad del Valle - Facultad de Ciencias - Departamento de Matem\u00e1ticas"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad del Valle - Facultad de Ciencias - Departamento de Matem\u00e1ticas","institution_ids":["https://openalex.org/I4210122576","https://openalex.org/I4210127437","https://openalex.org/I91732220"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11984088,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"1","first_page":"87","last_page":"107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.54830002784729,"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":0.54830002784729,"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":0.38179999589920044,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.025200000032782555,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/optical-fibers","display_name":"optical fibers","score":0.6890000104904175},{"id":"https://openalex.org/keywords/pulse-propagation","display_name":"pulse propagation","score":0.8790000081062317},{"id":"https://openalex.org/keywords/kerr-effect","display_name":"Kerr effect","score":0.9559999704360962},{"id":"https://openalex.org/keywords/hamiltonian-systems","display_name":"Hamiltonian systems","score":0.9850000143051147},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.7020000219345093},{"id":"https://openalex.org/keywords/newton-s-method","display_name":"Newton's method","score":0.6740000247955322},{"id":"https://openalex.org/keywords/nonlinear-schrodinger-equation","display_name":"nonlinear Schr\u00f6dinger equation","score":0.8500000238418579}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7193027138710022},{"id":"https://openalex.org/C199956316","wikidata":"https://www.wikidata.org/wiki/Q123300","display_name":"Standing wave","level":2,"score":0.7050408124923706},{"id":"https://openalex.org/C194232370","wikidata":"https://www.wikidata.org/wiki/Q162","display_name":"Optical fiber","level":2,"score":0.5084782838821411},{"id":"https://openalex.org/C2780167933","wikidata":"https://www.wikidata.org/wiki/Q1550652","display_name":"Pulse (music)","level":3,"score":0.45156267285346985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4437543749809265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43512266874313354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4277823269367218},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.33854979276657104},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.21132555603981018},{"id":"https://openalex.org/C94915269","wikidata":"https://www.wikidata.org/wiki/Q1834857","display_name":"Detector","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.15446/recolma.v53n1.81045","doi":"https://doi.org/10.15446/recolma.v53n1.81045","is_oa":true,"landing_page_url":"https://doi.org/10.15446/recolma.v53n1.81045","pdf_url":null,"source":{"id":"https://openalex.org/S4210171540","display_name":"Revista Colombiana de Matem\u00e1ticas","issn_l":"0034-7426","issn":["0034-7426","2357-4100"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","publindex-c","russia-white-list-4"],"host_organization":"https://openalex.org/P4310318911","host_organization_name":"National University of Colombia","host_organization_lineage":["https://openalex.org/P4310318911"],"host_organization_lineage_names":["National University of Colombia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Colombiana de Matem\u00e1ticas","raw_type":"journal-article"},{"id":"pmh:oai:ojs.unal.edu.co:article/81045","doi":null,"is_oa":true,"landing_page_url":"https://revistas.unal.edu.co/index.php/recolma/article/view/81045","pdf_url":"https://revistas.unal.edu.co/index.php/recolma/article/download/81045/71565","source":{"id":"https://openalex.org/S4210171540","display_name":"Revista Colombiana de Matem\u00e1ticas","issn_l":"0034-7426","issn":["0034-7426","2357-4100"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","publindex-c","russia-white-list-4"],"host_organization":"https://openalex.org/P4310318911","host_organization_name":"National University of Colombia","host_organization_lineage":["https://openalex.org/P4310318911"],"host_organization_lineage_names":["National University of Colombia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"0034-7426","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:www.revistas.unal.edu.co:article/81045","doi":null,"is_oa":false,"landing_page_url":"https://revistas.unal.edu.co/index.php/recolma/article/view/81045","pdf_url":null,"source":{"id":"https://openalex.org/S4377196295","display_name":"Magazine Portal Bibliotech Digital (Universidad Nacional de Colombia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I36243813","host_organization_name":"Universidad Nacional de Colombia","host_organization_lineage":["https://openalex.org/I36243813"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Colombiana de Matem\u00e1ticas; Vol. 53 N\u00fam. 1 (2019); 87-107","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.15446/recolma.v53n1.81045","doi":"https://doi.org/10.15446/recolma.v53n1.81045","is_oa":true,"landing_page_url":"https://doi.org/10.15446/recolma.v53n1.81045","pdf_url":null,"source":{"id":"https://openalex.org/S4210171540","display_name":"Revista Colombiana de Matem\u00e1ticas","issn_l":"0034-7426","issn":["0034-7426","2357-4100"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1","poland-20","publindex-c","russia-white-list-4"],"host_organization":"https://openalex.org/P4310318911","host_organization_name":"National University of Colombia","host_organization_lineage":["https://openalex.org/P4310318911"],"host_organization_lineage_names":["National University of Colombia"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Revista Colombiana de Matem\u00e1ticas","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6500097189","display_name":null,"funder_award_id":"100-00","funder_id":"https://openalex.org/F4320324328","funder_display_name":"Universidad del Valle"}],"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/F4320324328","display_name":"Universidad del Valle","ror":"https://ror.org/00jb9vg53"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W149201185","https://openalex.org/W1595000965","https://openalex.org/W1663357484","https://openalex.org/W1966770088","https://openalex.org/W1973783122","https://openalex.org/W1974872963","https://openalex.org/W1977942255","https://openalex.org/W1989405811","https://openalex.org/W1990677510","https://openalex.org/W2005317720","https://openalex.org/W2006003982","https://openalex.org/W2031211082","https://openalex.org/W2033027256","https://openalex.org/W2039743577","https://openalex.org/W2046522853","https://openalex.org/W2052963830","https://openalex.org/W2063221661","https://openalex.org/W2068525462","https://openalex.org/W2069054569","https://openalex.org/W2074913066","https://openalex.org/W2075685495","https://openalex.org/W2087581458","https://openalex.org/W2089025400","https://openalex.org/W2090885565","https://openalex.org/W2124529968","https://openalex.org/W2133286772","https://openalex.org/W2136215540","https://openalex.org/W2154195688","https://openalex.org/W2160230431","https://openalex.org/W2274890641","https://openalex.org/W2320231686","https://openalex.org/W2336017786","https://openalex.org/W2998476915","https://openalex.org/W4246906787","https://openalex.org/W4296477255","https://openalex.org/W4300907758","https://openalex.org/W6629776154","https://openalex.org/W6631374731","https://openalex.org/W6696838512","https://openalex.org/W6835342102"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1971388572","https://openalex.org/W1507702947"],"abstract_inverted_index":{"We":[0],"establish":[1],"existence":[2],"of":[3,14,54,73],"periodic":[4],"standing":[5,42,74],"waves":[6],"for":[7],"a":[8,15,49,61,66],"model":[9],"to":[10,69,82],"describe":[11],"the":[12,25,33,40,71],"propagation":[13],"light":[16],"pulse":[17],"inside":[18],"an":[19],"optical":[20],"fiber":[21],"taking":[22,37],"into":[23],"account":[24],"Kerr":[26],"effect.":[27],"To":[28],"this":[29],"end,":[30],"we":[31],"apply":[32],"Lyapunov":[34],"Center":[35],"Theorem":[36],"advantage":[38],"that":[39],"corresponding":[41],"wave":[43,75],"equations":[44],"can":[45],"be":[46,83],"rewritten":[47],"as":[48],"Hamiltonian":[50],"system.":[51],"Furthermore,":[52],"some":[53],"these":[55],"solutions":[56],"are":[57,80],"approximated":[58],"by":[59],"using":[60],"Newton-type":[62],"iteration,":[63],"combined":[64],"with":[65,86],"collocation-spectral":[67],"strategy":[68],"discretize":[70],"system":[72],"equations.":[76],"Our":[77],"numerical":[78],"simulations":[79],"found":[81],"in":[84],"accordance":[85],"our":[87],"analytical":[88],"results.":[89]},"counts_by_year":[],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}