{"id":"https://openalex.org/W1971478048","doi":"https://doi.org/10.1137/040618977","title":"Relative Periodic Solutions of the Complex Ginzburg--Landau Equation","display_name":"Relative Periodic Solutions of the Complex Ginzburg--Landau Equation","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1971478048","doi":"https://doi.org/10.1137/040618977","mag":"1971478048"},"language":"en","primary_location":{"id":"doi:10.1137/040618977","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040618977","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/nlin/0408018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101604645","display_name":"Vanessa L\u00f3pez","orcid":"https://orcid.org/0009-0006-3952-4663"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vanessa L\u00f3pez","raw_affiliation_strings":["University of Illinois at Urbana\u2013Champaign","Lawrence Berkeley National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana\u2013Champaign","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Lawrence Berkeley National Laboratory","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026032313","display_name":"Philip Boyland","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Philip Boyland","raw_affiliation_strings":["[University of Florida]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[University of Florida]","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112778840","display_name":"Michael T. Heath","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael T. Heath","raw_affiliation_strings":["University of Illinois at Urbana Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011004406","display_name":"Robert Moser","orcid":"https://orcid.org/0000-0001-7735-1253"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert D. Moser","raw_affiliation_strings":["Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL, USA. Cur"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Theoretical and Applied Mechanics, University of Illinois, Urbana, IL, USA. Cur","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6432,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.86161578,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"4","issue":"4","first_page":"1042","last_page":"1075"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9819999933242798,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9793999791145325,"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/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.7791745066642761},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6673088073730469},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6027957201004028},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5399117469787598},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.514635443687439},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.500603199005127},{"id":"https://openalex.org/keywords/periodic-sequence","display_name":"Periodic sequence","score":0.5003244876861572},{"id":"https://openalex.org/keywords/periodic-function","display_name":"Periodic function","score":0.4858984351158142},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48139524459838867},{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.46385928988456726},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4515773355960846},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4422367811203003},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4354541599750519},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18609189987182617},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10123211145401001}],"concepts":[{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.7791745066642761},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6673088073730469},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6027957201004028},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5399117469787598},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.514635443687439},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.500603199005127},{"id":"https://openalex.org/C120241303","wikidata":"https://www.wikidata.org/wiki/Q3503302","display_name":"Periodic sequence","level":2,"score":0.5003244876861572},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.4858984351158142},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48139524459838867},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.46385928988456726},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4515773355960846},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4422367811203003},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4354541599750519},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18609189987182617},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10123211145401001},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/040618977","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040618977","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:nlin/0408018","is_oa":true,"landing_page_url":"http://arxiv.org/abs/nlin/0408018","pdf_url":"https://arxiv.org/pdf/nlin/0408018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.7994","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.7994","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/nlin/0408018v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.3779","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.3779","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/nlin/0408018v2.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:nlin/0408018","is_oa":true,"landing_page_url":"http://arxiv.org/abs/nlin/0408018","pdf_url":"https://arxiv.org/pdf/nlin/0408018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W122965473","https://openalex.org/W1410980234","https://openalex.org/W1479875173","https://openalex.org/W1510014639","https://openalex.org/W1511670827","https://openalex.org/W1524590822","https://openalex.org/W1536237323","https://openalex.org/W1594759473","https://openalex.org/W1603139886","https://openalex.org/W1606340521","https://openalex.org/W1642891744","https://openalex.org/W1965778005","https://openalex.org/W1971172371","https://openalex.org/W1976921279","https://openalex.org/W1977296565","https://openalex.org/W1978800858","https://openalex.org/W1982387535","https://openalex.org/W1983231861","https://openalex.org/W1988055686","https://openalex.org/W1995694419","https://openalex.org/W1998148410","https://openalex.org/W1999281566","https://openalex.org/W2002094651","https://openalex.org/W2002542829","https://openalex.org/W2004021828","https://openalex.org/W2008000547","https://openalex.org/W2008486579","https://openalex.org/W2016067905","https://openalex.org/W2017585699","https://openalex.org/W2028810187","https://openalex.org/W2034963843","https://openalex.org/W2043892510","https://openalex.org/W2046253768","https://openalex.org/W2051854440","https://openalex.org/W2060934939","https://openalex.org/W2065198439","https://openalex.org/W2068484625","https://openalex.org/W2069792981","https://openalex.org/W2070734043","https://openalex.org/W2081817659","https://openalex.org/W2083490131","https://openalex.org/W2087070363","https://openalex.org/W2087106283","https://openalex.org/W2091468007","https://openalex.org/W2092188472","https://openalex.org/W2096070062","https://openalex.org/W2119627182","https://openalex.org/W2125178009","https://openalex.org/W2130714194","https://openalex.org/W2131778920","https://openalex.org/W2154893616","https://openalex.org/W2155576832","https://openalex.org/W2236623899","https://openalex.org/W2256578114","https://openalex.org/W2290515516","https://openalex.org/W2334170914","https://openalex.org/W2408478130","https://openalex.org/W2592381737","https://openalex.org/W3028277944","https://openalex.org/W3105220030","https://openalex.org/W3105337965","https://openalex.org/W4230402175","https://openalex.org/W4230836784","https://openalex.org/W4255469585","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2354390312","https://openalex.org/W4312337410","https://openalex.org/W2042117772","https://openalex.org/W1987281836","https://openalex.org/W4365814832","https://openalex.org/W2385169700","https://openalex.org/W1497028617","https://openalex.org/W2387516466","https://openalex.org/W2899623343","https://openalex.org/W1994161452"],"abstract_inverted_index":{"A":[0,35],"method":[1,61],"of":[2,54,88,114,120,147,155],"finding":[3],"relative":[4,21,36,63,103,148],"periodic":[5,22,32,37,44,64,104,149],"orbits":[6],"for":[7,24,92,107],"differential":[8],"equations":[9,91],"with":[10,31,117],"continuous":[11],"symmetries":[12],"is":[13,39,43],"described":[14],"and":[15,80,98,130],"its":[16],"utility":[17],"demonstrated":[18],"by":[19,51,68],"computing":[20],"solutions":[23,65,84,105,150],"the":[25,55,60,76,93,108,118,145,153],"one-dimensional":[26],"complex":[27],"Ginzburg--Landau":[28],"equation":[29],"(CGLE)":[30],"boundary":[33],"conditions.":[34],"solution":[38,41],"a":[40,49,69,86,111],"that":[42,141],"in":[45],"time,":[46],"up":[47],"to":[48,74,85,128,136],"transformation":[50],"an":[52],"element":[53,79],"equation's":[56],"symmetry":[57,77],"group.":[58],"With":[59],"used,":[62],"are":[66,81],"represented":[67],"space-time":[70],"Fourier":[71,94],"series":[72],"modified":[73],"include":[75],"group":[78,96],"sought":[82],"as":[83],"system":[87],"nonlinear":[89],"algebraic":[90],"coefficients,":[95],"element,":[97],"time":[99],"period.":[100],"The":[101],"77":[102],"found":[106],"CGLE":[109],"exhibit":[110],"wide":[112],"variety":[113],"temporal":[115],"dynamics,":[116],"sum":[119],"their":[121,131],"positive":[122],"Lyapunov":[123],"exponents":[124],"varying":[125],"from":[126,134],"5.19":[127],"60.35":[129],"unstable":[132],"dimensions":[133],"3":[135],"8.":[137],"Preliminary":[138],"work":[139],"indicates":[140],"weighted":[142],"averages":[143],"over":[144],"collection":[146],"accurately":[151],"approximate":[152],"value":[154],"several":[156],"functionals":[157],"on":[158],"typical":[159],"trajectories.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"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"}
