{"id":"https://openalex.org/W2114094448","doi":"https://doi.org/10.1155/2012/605687","title":"The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System","display_name":"The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2114094448","doi":"https://doi.org/10.1155/2012/605687","mag":"2114094448"},"language":"en","primary_location":{"id":"doi:10.1155/2012/605687","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/605687","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2012/605687.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/ijmms/2012/605687.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070529210","display_name":"Victor F. Dailyudenko","orcid":null},"institutions":[{"id":"https://openalex.org/I4210105192","display_name":"United Institute of Informatics Problems","ror":"https://ror.org/01ccbsb07","country_code":"BY","type":"facility","lineage":["https://openalex.org/I151823869","https://openalex.org/I4210105192","https://openalex.org/I4210116091"]},{"id":"https://openalex.org/I151823869","display_name":"National Academy of Sciences of Belarus","ror":"https://ror.org/02j8pe645","country_code":"BY","type":"government","lineage":["https://openalex.org/I151823869"]}],"countries":["BY"],"is_corresponding":true,"raw_author_name":"Victor F. Dailyudenko","raw_affiliation_strings":["United Institute of Informatics Problems of the National Academy of Sciences of Belarus, Surganov Street 6, 220012, Minsk, Belarus"],"affiliations":[{"raw_affiliation_string":"United Institute of Informatics Problems of the National Academy of Sciences of Belarus, Surganov Street 6, 220012, Minsk, Belarus","institution_ids":["https://openalex.org/I4210105192","https://openalex.org/I151823869"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070529210"],"corresponding_institution_ids":["https://openalex.org/I151823869","https://openalex.org/I4210105192"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.18917458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2012","issue":null,"first_page":"1","last_page":"17"},"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/T13362","display_name":"Slime Mold and Myxomycetes Research","score":0.9717000126838684,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9605000019073486,"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/mathematics","display_name":"Mathematics","score":0.8281188011169434},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7572851777076721},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.7239804267883301},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6397032737731934},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.620465099811554},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.5157464146614075},{"id":"https://openalex.org/keywords/third-order","display_name":"Third order","score":0.4594790041446686},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.42851364612579346},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35724490880966187},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1760847568511963},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08812066912651062}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8281188011169434},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7572851777076721},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.7239804267883301},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6397032737731934},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.620465099811554},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.5157464146614075},{"id":"https://openalex.org/C2777566824","wikidata":"https://www.wikidata.org/wiki/Q1259252","display_name":"Third order","level":2,"score":0.4594790041446686},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.42851364612579346},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35724490880966187},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1760847568511963},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08812066912651062},{"id":"https://openalex.org/C27206212","wikidata":"https://www.wikidata.org/wiki/Q34178","display_name":"Theology","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/605687","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/605687","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2012/605687.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:605687","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2012/605687.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:416755cc6c084ba086c733497bf9022f","is_oa":true,"landing_page_url":"https://doaj.org/article/416755cc6c084ba086c733497bf9022f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2012 (2012)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2012/605687","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/605687","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2012/605687","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2012/605687","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2012/605687.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2114094448.pdf","grobid_xml":"https://content.openalex.org/works/W2114094448.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W45781964","https://openalex.org/W1584724822","https://openalex.org/W1964193846","https://openalex.org/W1995693674","https://openalex.org/W1999493972","https://openalex.org/W2004229046","https://openalex.org/W2022337355","https://openalex.org/W2026011981","https://openalex.org/W2034862878","https://openalex.org/W2035369370","https://openalex.org/W2040696052","https://openalex.org/W2040749202","https://openalex.org/W2047023174","https://openalex.org/W2053733083","https://openalex.org/W2063215580","https://openalex.org/W2074771676","https://openalex.org/W2077653620","https://openalex.org/W2086126894","https://openalex.org/W2113558285","https://openalex.org/W2162356158","https://openalex.org/W2171466642"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2070252991","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W2803761277","https://openalex.org/W2013089105","https://openalex.org/W2048057206","https://openalex.org/W2364723928"],"abstract_inverted_index":{"By":[0],"investigation":[1],"of":[2,36,44,66,87,105],"perturbation":[3],"solution":[4],"for":[5,14,39],"nonlinear":[6,45],"reaction-diffusion":[7],"system,":[8],"we":[9],"derive":[10],"related":[11,96],"differential":[12],"model":[13,29],"perturbations":[15],"that":[16],"involves":[17],"weak":[18],"nonlinearities":[19],"up":[20],"to":[21,32],"third":[22],"order.":[23],"For":[24],"a":[25],"first":[26],"time,":[27],"this":[28],"is":[30],"shown":[31],"result":[33],"in":[34,50,92],"derivation":[35,104],"the":[37,64,84,88,103,106],"system":[38,56],"amplitude":[40],"distribution":[41],"by":[42],"means":[43],"integration":[46],"on":[47],"orthogonal":[48],"basis":[49],"spatial":[51],"region.":[52],"The":[53,95],"obtained":[54],"time-dependent":[55],"(TDS)":[57],"contains":[58],"all":[59],"possible":[60],"functional":[61],"relations":[62],"between":[63],"modes":[65],"wave":[67],"train":[68],"under":[69],"consideration":[70],"along":[71],"with":[72],"delayed":[73],"relations,":[74],"and":[75,98],"after":[76],"numerical":[77],"simulation":[78],"it":[79],"provides":[80],"some":[81],"conclusions":[82],"concerning":[83],"natural":[85],"frequency":[86],"investigated":[89],"self-organization":[90],"process":[91],"active":[93],"medium.":[94],"matrix":[97],"modulo":[99],"operations":[100],"which":[101],"substantiate":[102],"TDS":[107],"are":[108],"also":[109],"considered.":[110]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
