{"id":"https://openalex.org/W2011355267","doi":"https://doi.org/10.1137/s0036139994277531","title":"Pattern Formation in Systems with Slowly Varying Geometry","display_name":"Pattern Formation in Systems with Slowly Varying Geometry","publication_year":1997,"publication_date":"1997-02-01","ids":{"openalex":"https://openalex.org/W2011355267","doi":"https://doi.org/10.1137/s0036139994277531","mag":"2011355267"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139994277531","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139994277531","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/A5070081332","display_name":"Rachel Kuske","orcid":"https://orcid.org/0000-0002-7140-0365"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rachel Kuske","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066808911","display_name":"Wiktor Eckhaus","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wiktor Eckhaus","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0149,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.80607691,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"57","issue":"1","first_page":"112","last_page":"152"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9983999729156494,"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":0.9983999729156494,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9772999882698059,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6981654763221741},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6725871562957764},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.6558501720428467},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6043893098831177},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5097593665122986},{"id":"https://openalex.org/keywords/modulation","display_name":"Modulation (music)","score":0.5056726932525635},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4408855736255646},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4219071865081787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2787312865257263},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1363595426082611}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6981654763221741},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6725871562957764},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.6558501720428467},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6043893098831177},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5097593665122986},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.5056726932525635},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4408855736255646},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4219071865081787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2787312865257263},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1363595426082611},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139994277531","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139994277531","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W39996637","https://openalex.org/W1739266651","https://openalex.org/W1964275593","https://openalex.org/W1964387209","https://openalex.org/W1973152619","https://openalex.org/W1974987310","https://openalex.org/W1992749670","https://openalex.org/W2004817102","https://openalex.org/W2009611722","https://openalex.org/W2014719155","https://openalex.org/W2019923694","https://openalex.org/W2024293975","https://openalex.org/W2029163709","https://openalex.org/W2034397106","https://openalex.org/W2042914847","https://openalex.org/W2054571151","https://openalex.org/W2072059296","https://openalex.org/W2080563946","https://openalex.org/W2094841526","https://openalex.org/W2103098521","https://openalex.org/W2107496770","https://openalex.org/W2109516935","https://openalex.org/W2119347661","https://openalex.org/W2142343282","https://openalex.org/W2149453355","https://openalex.org/W2154888593","https://openalex.org/W2214892346","https://openalex.org/W2555719866","https://openalex.org/W3129495151"],"related_works":["https://openalex.org/W3086618278","https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2006100586","https://openalex.org/W4300809132","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W2103373899"],"abstract_inverted_index":{"A":[0],"class":[1],"of":[2,10,46,57,60,76,128,146],"equations":[3,90],"is":[4,51,185],"considered":[5],"which":[6,65,180],"describe":[7],"the":[8,44,110,126,129,134,147],"evolution":[9],"patterns":[11],"in":[12,48,125],"problems":[13],"with":[14],"a":[15,22,32,68,181],"geometry":[16,81,109],"varying":[17,80,86,108,138],"slightly,":[18,78,83,106,135],"as":[19],"characterized":[20],"by":[21,43],"small":[23],"parameter":[24],"$\\tilde":[25],"\\nu\\ll":[26],"1":[27],"$,":[28],"and":[29,62,82,102,121,158],"slowly,":[30],"on":[31],"spatial":[33],"scale":[34],"$\\hat\\epsilon":[35],"x$":[36],"for":[37,53,150,153,162,179],"$\\hat\\epsilon\\ll":[38],"1$.":[39],"The":[40],"model,":[41],"inspired":[42],"problem":[45],"sedimentation":[47],"meandering":[49],"rivers,":[50],"generalized":[52],"an":[54,167],"analytical":[55,96],"study":[56],"nonlinear":[58,130],"dynamics":[59],"periodic":[61,144],"quasi-periodic":[63,117],"solutions":[64,118,145,161],"bifurcate":[66],"from":[67],"basic":[69,111],"solution.":[70],"Two":[71],"cases":[72],"prove":[73],"to":[74,99,116],"be":[75],"interest:":[77],"slowly":[79,85,107,137],"very":[84,136],"geometry.":[87],"Nonlinear":[88],"modulation":[89,131,148],"are":[91,123,141,175],"studied":[92,124],"foreach":[93],"case,":[94],"yielding":[95],"results":[97],"complimentary":[98],"previous":[100],"linear":[101],"numerical":[103],"analyses.":[104],"For":[105],"solution":[112],"loses":[113],"its":[114],"stability":[115,122],"whose":[119],"existence":[120],"context":[127],"equation.":[132],"In":[133,166],"case":[139],"there":[140,174],"stationary":[142],"spatially":[143],"equation":[149],"all":[151],"x":[152],"values":[154],"$R":[155,163],">":[156],"R_{max}$":[157,173],"no":[159],"such":[160],"<":[164,170,172],"R_{cr}$.":[165],"interval":[168],"$R_{cr}":[169],"R":[171],"stable":[176],"localized":[177],"structures":[178],"uniform":[182],"asymptotic":[183],"approximation":[184],"constructed":[186],"analytically.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
