{"id":"https://openalex.org/W3208972432","doi":"https://doi.org/10.1137/21m1455760","title":"Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations","display_name":"Stability of Traveling Oscillating Fronts in Complex Ginzburg Landau Equations","publication_year":2022,"publication_date":"2022-09-26","ids":{"openalex":"https://openalex.org/W3208972432","doi":"https://doi.org/10.1137/21m1455760","mag":"3208972432"},"language":"en","primary_location":{"id":"doi:10.1137/21m1455760","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1455760","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5110164030","display_name":"Wolf\u2010J\u00fcrgen Beyn","orcid":null},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Wolf-J\u00fcrgen Beyn","raw_affiliation_strings":["Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Bielefeld University, 33501 Bielefeld, Germany,","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065276250","display_name":"Christian D\u00f6ding","orcid":"https://orcid.org/0000-0001-5641-4585"},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian D\u00f6ding","raw_affiliation_strings":["Department of Mathematics, Ruhr-University Bochum, 44801 Bochum, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ruhr-University Bochum, 44801 Bochum, Germany,","institution_ids":["https://openalex.org/I904495901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5344,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63962129,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"54","issue":"5","first_page":"5447","last_page":"5488"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9929999709129333,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8135217428207397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5883002281188965},{"id":"https://openalex.org/keywords/essential-spectrum","display_name":"Essential spectrum","score":0.5568241477012634},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.49638205766677856},{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.48705318570137024},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.47771716117858887},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.4774768352508545},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.4524874985218048},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.44483017921447754},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4310700297355652},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.41195017099380493},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19995146989822388},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1789972186088562},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12345382571220398}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8135217428207397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5883002281188965},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.5568241477012634},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49638205766677856},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.48705318570137024},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.47771716117858887},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.4774768352508545},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.4524874985218048},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.44483017921447754},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4310700297355652},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.41195017099380493},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19995146989822388},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1789972186088562},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12345382571220398}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1455760","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1455760","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8651366121","display_name":null,"funder_award_id":"SFB 1283/2 2021 - 317210226","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323389","display_name":"Universit\u00e4t Bielefeld","ror":"https://ror.org/02hpadn98"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W32950421","https://openalex.org/W35304917","https://openalex.org/W141185090","https://openalex.org/W163224475","https://openalex.org/W355012799","https://openalex.org/W360456325","https://openalex.org/W607590176","https://openalex.org/W1481457519","https://openalex.org/W1487057719","https://openalex.org/W1560060148","https://openalex.org/W1562265198","https://openalex.org/W1966250520","https://openalex.org/W1966821511","https://openalex.org/W1967308282","https://openalex.org/W1971808848","https://openalex.org/W1981968943","https://openalex.org/W1985698439","https://openalex.org/W1996849700","https://openalex.org/W2000436005","https://openalex.org/W2002094651","https://openalex.org/W2004518404","https://openalex.org/W2005761796","https://openalex.org/W2028001433","https://openalex.org/W2029367552","https://openalex.org/W2031743529","https://openalex.org/W2044397518","https://openalex.org/W2052172730","https://openalex.org/W2065364553","https://openalex.org/W2077988770","https://openalex.org/W2093201093","https://openalex.org/W2106871975","https://openalex.org/W2116376797","https://openalex.org/W2127341386","https://openalex.org/W2492505543","https://openalex.org/W2579246540","https://openalex.org/W3101412341","https://openalex.org/W3154079207","https://openalex.org/W3208103518","https://openalex.org/W3209222329","https://openalex.org/W4313905188"],"related_works":["https://openalex.org/W2945455047","https://openalex.org/W2106070738","https://openalex.org/W2040585115","https://openalex.org/W2347535072","https://openalex.org/W2952745759","https://openalex.org/W2349083538","https://openalex.org/W2165516351","https://openalex.org/W1968201932","https://openalex.org/W2008373210","https://openalex.org/W2374488874"],"abstract_inverted_index":{"Traveling":[0],"oscillating":[1],"fronts":[2],"(TOFs)":[3],"are":[4,144],"specific":[5],"one-dimensional":[6],"waves":[7],"of":[8,58,78,90,154],"the":[9,59,75,83,88,114,120,132,148,155,160,169,173,177,188],"form":[10],"$U_\\star":[11],"(x,t)":[12],"=":[13,62],"e^{-i":[14],"\\omega":[15],"t}":[16],"V_\\star(x":[17],"-":[18],"ct)$":[19],"with":[20],"a":[21,32,72,96,101,123,136],"complex-valued":[22],"profile":[23],"$V_{\\star}$":[24],"that":[25,113,140],"decays":[26],"at":[27,35,106,180],"$-":[28],"\\infty$":[29],"but":[30,103],"approaches":[31,100],"nonzero":[33,104],"limit":[34,105],"$+\\infty$.":[36],"In":[37,67],"particular,":[38],"we":[39,70,81],"consider":[40,159],"TOFs":[41],"which":[42,50,99,167],"connect":[43],"two":[44],"stable":[45],"homogeneous":[46],"rest":[47],"states":[48],"and":[49,95,125,139,199],"occur":[51],"generically":[52],"in":[53,122,135,162],"complex":[54],"Ginzburg":[55],"Landau":[56],"equations":[57],"type":[60],"$U_t":[61],"\\alpha":[63],"U_{xx}":[64],"+":[65],"G(|U|^2)U$.":[66],"this":[68],"paper":[69],"prove":[71],"theorem":[73],"on":[74,172],"asymptotic":[76],"stability":[77],"TOFs,":[79],"where":[80],"allow":[82],"initial":[84],"perturbation":[85],"to":[86,158,176,192],"be":[87],"sum":[89],"an":[91,163],"exponentially":[92],"localized":[93],"part":[94,98],"front-like":[97],"small":[102],"$+":[107,181],"\\infty$.":[108,182],"The":[109,151],"underlying":[110],"assumptions":[111],"guarantee":[112],"operator,":[115],"obtained":[116],"from":[117,147],"linearizing":[118],"about":[119],"TOF":[121],"co-moving":[124],"co-rotating":[126],"frame,":[127],"has":[128],"essential":[129],"spectrum":[130],"touching":[131],"imaginary":[133,149],"axis":[134],"quadratic":[137],"fashion":[138],"further":[141],"isolated":[142],"eigenvalues":[143],"bounded":[145],"away":[146],"axis.":[150],"basic":[152],"idea":[153],"proof":[156],"is":[157],"problem":[161],"extended":[164],"phase":[165],"space":[166],"couples":[168],"wave":[170],"dynamics":[171,179],"real":[174],"line":[175],"ODE":[178],"Using":[183],"slowly":[184],"decaying":[185],"exponential":[186],"weights,":[187],"framework":[189],"allows":[190],"one":[191],"derive":[193],"appropriate":[194],"resolvent":[195],"estimates,":[196],"semigroup":[197],"techniques,":[198],"Gronwall":[200],"estimates.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}