{"id":"https://openalex.org/W2162423966","doi":"https://doi.org/10.1137/s0036139992233938","title":"Computation and Stability of Fluxons in a Singularly Perturbed Sine-Gordon Model of the Josephson Junction","display_name":"Computation and Stability of Fluxons in a Singularly Perturbed Sine-Gordon Model of the Josephson Junction","publication_year":1994,"publication_date":"1994-08-01","ids":{"openalex":"https://openalex.org/W2162423966","doi":"https://doi.org/10.1137/s0036139992233938","mag":"2162423966"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139992233938","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139992233938","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","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/A5100684198","display_name":"David L. Brown","orcid":"https://orcid.org/0000-0002-9505-2959"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David L. Brown","raw_affiliation_strings":["Los Alamos national Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos national Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030886600","display_name":"M. Gregory Forest","orcid":"https://orcid.org/0000-0002-7718-4456"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Gregory Forest","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039373170","display_name":"Brian J. Miller","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brian J. Miller","raw_affiliation_strings":["Los Alamos national Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos national Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008289430","display_name":"N. Anders Petersson","orcid":"https://orcid.org/0000-0003-0522-7872"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Anders Petersson","raw_affiliation_strings":["Los Alamos national Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Los Alamos national Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6474,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.84518892,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"4","first_page":"1048","last_page":"1066"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9976999759674072,"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"}},"topics":[{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9976999759674072,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9944000244140625,"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/fluxon","display_name":"Fluxon","score":0.9653792381286621},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6591084003448486},{"id":"https://openalex.org/keywords/josephson-effect","display_name":"Josephson effect","score":0.6128600835800171},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.46935683488845825},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4526195824146271},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.44508078694343567},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4281577467918396},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.4110386371612549},{"id":"https://openalex.org/keywords/superconductivity","display_name":"Superconductivity","score":0.3544592559337616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31840938329696655},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2698288559913635},{"id":"https://openalex.org/keywords/pi-josephson-junction","display_name":"Pi Josephson junction","score":0.2148706018924713}],"concepts":[{"id":"https://openalex.org/C53105130","wikidata":"https://www.wikidata.org/wiki/Q1068152","display_name":"Fluxon","level":5,"score":0.9653792381286621},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6591084003448486},{"id":"https://openalex.org/C12038964","wikidata":"https://www.wikidata.org/wiki/Q764228","display_name":"Josephson effect","level":3,"score":0.6128600835800171},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.46935683488845825},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4526195824146271},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.44508078694343567},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4281577467918396},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4110386371612549},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.3544592559337616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31840938329696655},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2698288559913635},{"id":"https://openalex.org/C180349316","wikidata":"https://www.wikidata.org/wiki/Q7189956","display_name":"Pi Josephson junction","level":4,"score":0.2148706018924713},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139992233938","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139992233938","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W54180077","https://openalex.org/W1971808848","https://openalex.org/W1973985780","https://openalex.org/W2014097108","https://openalex.org/W2028296976","https://openalex.org/W2047929780","https://openalex.org/W2054225095","https://openalex.org/W2055712310","https://openalex.org/W2065364553","https://openalex.org/W2074920889","https://openalex.org/W2163036037","https://openalex.org/W2163858007"],"related_works":["https://openalex.org/W1984846709","https://openalex.org/W4249010853","https://openalex.org/W2020818175","https://openalex.org/W2040112561","https://openalex.org/W2105322189","https://openalex.org/W2007811900","https://openalex.org/W1964608956","https://openalex.org/W2010603681","https://openalex.org/W2064643858","https://openalex.org/W2066163905"],"abstract_inverted_index":{"New":[0],"numerical":[1,34,61,152,168,285,361],"results":[2,286],"are":[3,145,216],"reported":[4],"regarding":[5],"the":[6,39,52,56,73,77,92,100,103,109,115,132,136,139,156,178,181,189,223,227,234,239,248,255,259,269,272,276,281,328,364],"solutions":[7,45,173,179,204],"of":[8,42,51,76,99,124,131,171,177,213,247,258,271,280],"a":[9,48,59,83,88,96,122,128,147,166,245],"singularly":[10],"perturbed":[11],"sine-Gordon":[12],"equation,":[13],"modeling":[14],"magnetic":[15],"flux":[16],"quanta":[17],"(fluxons)":[18],"in":[19,91,155,363],"long":[20],"Josephson":[21],"tunnel":[22],"junctions":[23],"with":[24,356],"nonzero":[25],"surface":[26],"impedance.":[27],"Previous":[28],"authors,":[29],"hampered":[30],"by":[31,149,159,210],"an":[32],"inadequate":[33],"shooting":[35],"method,":[36],"conjectured":[37],"that":[38,72,108,175,188,205,345],"fluxon":[40,199,236],"branch":[41],"solitary":[43,202],"wave":[44,203],"terminates":[46],"at":[47,114,138,244,275],"critical":[49,74,116,256],"value":[50,63,75,117,130,137,246,257,270],"bias":[53,78,104,133,249,273],"current.":[54],"In":[55],"present":[57],"paper,":[58],"new":[60],"boundary":[62],"solver":[64],"is":[65,185,252,344],"developed":[66],"and":[67,118,163,187],"then":[68,119],"used":[69],"to":[70,82,87,127],"show":[71],"current":[79,134,151,250,274],"corresponds":[80],"not":[81],"termination":[84],"point":[85,90,184,242,279],"but":[86],"turning":[89,125,141,183,196,241,278],"bifurcation":[93],"diagram.":[94],"Plotting":[95],"suitable":[97],"norm":[98],"solution":[101,110,190,220,326],"against":[102],"current,":[105],"we":[106,263],"find":[107],"curve":[111],"turns":[112],"back":[113],"oscillates":[120],"via":[121],"sequence":[123],"points":[126,208],"limiting":[129],"below":[135],"first":[140,182,240,277],"point.":[142,197],"These":[143],"conclusions":[144],"confirmed,":[146],"posteriors,":[148],"adapting":[150],"procedures":[153],"described":[154],"literature,":[157],"e.g.,":[158],"Beyn,":[160],"Doedel,":[161],"Friedman":[162],"others.":[164],"Furthermore,":[165],"careful":[167],"stability":[169],"analysis":[170],"these":[172,284],"shows":[174],"none":[176],"past":[180,349],"stable":[186],"acquires":[191],"one":[192],"additional":[193],"instability":[194],"per":[195],"Multiple":[198],"solutions,":[200],"i.e.,":[201],"connect":[206],"fixed":[207],"separated":[209],"integer":[211],"multiples":[212],"$2\\pi":[214],"$,":[215,294,308,325,353],"also":[217],"studied.":[218],"The":[219,339],"curves":[221],"for":[222,233,288,298,313,333],"multiple":[224],"fluxons":[225,296,311,347],"exhibit":[226],"same":[228],"qualitative":[229],"behavior":[230],"as":[231],"those":[232],"single":[235,260,310],"case.":[237],"However,":[238],"occurs":[243],"which":[251,354],"less":[253],"than":[254],"fluxon.":[261],"If":[262],"denote":[264],"by$\\gamma":[265],"_j^":[266],"*":[267,293,301,307,318,324,352],"$":[268],"j-fluxon":[282,329],"family,":[283],"suggest:":[287],"$\\gamma":[289,299,314,350],">":[290],"\\gamma":[291,303,305,320,322],"_1^":[292,306,351],"no":[295,346],"exist;":[297,312],"_2^":[300],"<":[302,304,319],"only":[309,332],"_{k":[315],"+":[316],"1}^":[317],"\\leq":[321],"_k^":[323],"from":[327],"family":[330],"exist":[331,348],"$j":[334],"=":[335],"1,2,":[336],"\\ldots":[337],",k$.":[338],"most":[340],"physically":[341],"relevant":[342],"conclusion":[343],"agrees":[355],"previous":[357],"reports":[358],"based":[359],"on":[360],"simulations":[362],"time-domain.":[365]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}