{"id":"https://openalex.org/W2046434373","doi":"https://doi.org/10.1137/s0036144597317418","title":"Collective Coordinates and Length-Scale Competition in Spatially Inhomogeneous Soliton-Bearing Equations","display_name":"Collective Coordinates and Length-Scale Competition in Spatially Inhomogeneous Soliton-Bearing Equations","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W2046434373","doi":"https://doi.org/10.1137/s0036144597317418","mag":"2046434373"},"language":"en","primary_location":{"id":"doi:10.1137/s0036144597317418","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144597317418","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5077285926","display_name":"\u00c1ngel S\u00e1nchez","orcid":"https://orcid.org/0000-0003-1874-2881"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Angel S\u00e1nchez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113506287","display_name":"A. R. Bishop","orcid":"https://orcid.org/0009-0002-4781-387X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. R. Bishop","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5218,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.93557905,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"40","issue":"3","first_page":"579","last_page":"615"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994000196456909,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994000196456909,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9991999864578247,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9965999722480774,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.7329248189926147},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.488693505525589},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.46292614936828613},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.43984392285346985},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4397435784339905},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3755313754081726},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3607289493083954},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.335022509098053},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.322053998708725},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3082317113876343},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.15757325291633606},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.095650315284729}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7329248189926147},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.488693505525589},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.46292614936828613},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.43984392285346985},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4397435784339905},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3755313754081726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3607289493083954},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.335022509098053},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.322053998708725},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3082317113876343},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.15757325291633606},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.095650315284729},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036144597317418","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036144597317418","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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":79,"referenced_works":["https://openalex.org/W21422078","https://openalex.org/W386140868","https://openalex.org/W640896904","https://openalex.org/W1510817630","https://openalex.org/W1631957514","https://openalex.org/W1639561984","https://openalex.org/W1661394736","https://openalex.org/W1963656706","https://openalex.org/W1965578162","https://openalex.org/W1966841514","https://openalex.org/W1971213823","https://openalex.org/W1972739465","https://openalex.org/W1973968478","https://openalex.org/W1976299911","https://openalex.org/W1977355685","https://openalex.org/W1981087173","https://openalex.org/W1985201135","https://openalex.org/W1986435512","https://openalex.org/W1986788497","https://openalex.org/W1987668201","https://openalex.org/W1988322580","https://openalex.org/W1991985412","https://openalex.org/W1992544831","https://openalex.org/W1993166169","https://openalex.org/W1994520194","https://openalex.org/W1995000834","https://openalex.org/W1995301992","https://openalex.org/W1999030449","https://openalex.org/W2001270606","https://openalex.org/W2010756036","https://openalex.org/W2015331834","https://openalex.org/W2017397470","https://openalex.org/W2021579602","https://openalex.org/W2022939093","https://openalex.org/W2024496227","https://openalex.org/W2028752291","https://openalex.org/W2030593486","https://openalex.org/W2035311210","https://openalex.org/W2035359309","https://openalex.org/W2041809586","https://openalex.org/W2043283648","https://openalex.org/W2050639649","https://openalex.org/W2051072483","https://openalex.org/W2051835609","https://openalex.org/W2053688108","https://openalex.org/W2054069258","https://openalex.org/W2060532935","https://openalex.org/W2061511829","https://openalex.org/W2066430552","https://openalex.org/W2069226173","https://openalex.org/W2071148459","https://openalex.org/W2072306326","https://openalex.org/W2078041165","https://openalex.org/W2078264261","https://openalex.org/W2078489318","https://openalex.org/W2080320808","https://openalex.org/W2087906621","https://openalex.org/W2089432750","https://openalex.org/W2089902507","https://openalex.org/W2092433776","https://openalex.org/W2094643410","https://openalex.org/W2097466331","https://openalex.org/W2108210777","https://openalex.org/W2115600080","https://openalex.org/W2118575947","https://openalex.org/W2122705104","https://openalex.org/W2140237377","https://openalex.org/W2140790342","https://openalex.org/W2148480806","https://openalex.org/W2161509760","https://openalex.org/W2170120409","https://openalex.org/W2171004426","https://openalex.org/W2431787210","https://openalex.org/W2483086400","https://openalex.org/W2493550332","https://openalex.org/W2606081778","https://openalex.org/W3103122390","https://openalex.org/W4232401238","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2044787408","https://openalex.org/W4249228129","https://openalex.org/W2040820615","https://openalex.org/W2086585817","https://openalex.org/W155593081","https://openalex.org/W2738038633","https://openalex.org/W1506619710","https://openalex.org/W2052607948","https://openalex.org/W2019140719","https://openalex.org/W1968454318"],"abstract_inverted_index":{"Perturbed,":[0],"one-dimensional,":[1],"integrable":[2,29,227],"(i.e.,":[3],"soliton-bearing)":[4],"equations":[5],"arise":[6],"in":[7,24,99,139,225,233,278],"many":[8],"applied":[9],"contexts":[10],"when":[11,33],"trying":[12],"to":[13,40,56,80,106,133,143,201,212,259],"improve":[14],"the":[15,27,34,50,57,65,82,88,97,103,111,118,141,144,148,159,186,191,195,219,234,248,261,264,275,291,298,309],"(usually":[16],"highly":[17],"idealized)":[18],"description":[19,273],"of":[20,22,26,90,93,117,126,158,161,185,194,221,244,247,263,274,283,297,311],"problems":[21],"interest":[23],"terms":[25],"purely":[28],"equations.":[30],"In":[31,60,167],"particular,":[32],"assumption":[35],"ofperfect":[36],"homogeneity":[37],"is":[38,150,256],"dropped":[39],"account":[41],"for":[42,87,218],"unavoidable":[43],"impurities":[44],"or":[45],"defects,":[46],"perturbations":[47],"depending":[48],"on":[49,110,305],"spatial":[51],"coordinate":[52,113],"must":[53],"be":[54,213],"added":[55],"original":[58],"equation.":[59],"this":[61,91,127,155,171,268],"review,":[62],"we":[63,101,210],"use":[64],"one-dimensional":[66],"sine-Gordon":[67],"(sG)":[68],"equation":[69,198],"perturbed":[70,226,250],"by":[71,242,267],"a":[72,77,181,203,214,295,302],"spatially":[73],"periodic":[74],"term":[75],"as":[76,115,229],"generic":[78],"paradigm":[79],"discuss":[81],"main":[83],"perturbative":[84,128,176,189],"techniques":[85,276],"available":[86],"study":[89],"class":[92],"problems.":[94],"To":[95,153,270],"place":[96],"work":[98],"context,":[100],"summarize":[102],"approaches":[104],"developed":[105],"date":[107],"and":[108,130,177,301],"focus":[109],"collective":[112,162],"approach":[114,172],"one":[116],"most":[119],"useful":[120],"tools.":[121],"We":[122,137],"introduce":[123,202],"several":[124],"versions":[125],"method":[129],"relate":[131],"them":[132],"more":[134],"involved":[135],"procedures.":[136],"analyze":[138],"detail":[140],"application":[142,160],"sG":[145,197],"equation,":[146],"but":[147],"procedure":[149],"very":[151,182],"general.":[152],"illustrate":[154],"other":[156,230],"examples":[157],"coordinates":[163],"are":[164,240,287],"briefly":[165],"revisited.":[166],"our":[168,272,284],"case":[169],"study,":[170],"helps":[173],"us":[174,200],"identify":[175],"nonperturbative":[178,238],"regimes,":[179],"yielding":[180],"simple":[183],"picture":[184],"former.":[187],"Beyond":[188],"calculations,":[190],"same":[192],"example":[193],"inhomogeneous":[196],"allows":[199],"phenomenon,":[204],"termed":[205],"length":[206],"scale":[207],"competition,":[208],"which":[209],"show":[211],"rather":[215],"general":[216,306],"mechanism":[217],"appearance":[220],"complex":[222],"spatiotemporal":[223],"behavior":[224],"systems,":[228],"instances":[231],"discussed":[232],"review":[235],"show.":[236],"Such":[237],"results":[239],"obtained":[241],"means":[243],"numerical":[245,252,285],"simulations":[246,286],"full":[249],"problem;":[251],"linear":[253],"stability":[254],"analysis":[255],"also":[257,288],"used":[258],"clarify":[260],"origins":[262],"instability":[265],"originated":[266],"competition.":[269],"complement":[271],"employed":[277],"these":[279],"studies,":[280],"computational":[281],"details":[282],"included.":[289],"Finally,":[290],"paper":[292],"closes":[293],"with":[294,313],"discussion":[296],"above":[299],"ideas":[300],"speculative":[303],"outlook":[304],"questions":[307],"concerning":[308],"interplay":[310],"nonlinearity":[312],"disorder.":[314]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"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"}