{"id":"https://openalex.org/W2018094870","doi":"https://doi.org/10.1134/s1061920809020083","title":"Construction of uniform asymptotic solutions of wave-type differential equations by methods of catastrophe theory","display_name":"Construction of uniform asymptotic solutions of wave-type differential equations by methods of catastrophe theory","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2018094870","doi":"https://doi.org/10.1134/s1061920809020083","mag":"2018094870"},"language":"en","primary_location":{"id":"doi:10.1134/s1061920809020083","doi":"https://doi.org/10.1134/s1061920809020083","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1061920809020083","pdf_url":null,"source":{"id":"https://openalex.org/S121350373","display_name":"Russian Journal of Mathematical Physics","issn_l":"1061-9208","issn":["1061-9208","1555-6638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Russian Journal of Mathematical Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5066525440","display_name":"A. S. Kryukovsky","orcid":"https://orcid.org/0000-0001-5670-0354","observed_orcids":["https://orcid.org/0000-0001-5670-0354","https://orcid.org/0000-0001-9465-6040"]},"institutions":[{"id":"https://openalex.org/I3129897247","display_name":"Russian New University","ror":"https://ror.org/00gj2kk32","country_code":"RU","type":"education","lineage":["https://openalex.org/I3129897247"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. S. Kryukovskii","raw_affiliation_strings":["Russian New University, Moscow, Russia","Russian New University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Russian New University, Moscow, Russia","institution_ids":["https://openalex.org/I3129897247"]},{"raw_affiliation_string":"Russian New University","institution_ids":["https://openalex.org/I3129897247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070037859","display_name":"D. S. Lukin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"D. S. Lukin","raw_affiliation_strings":["Moscow Institute of Physics and Technology, Moscow, Russia","Moscow institute of physics and technology;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Moscow Institute of Physics and Technology, Moscow, Russia","institution_ids":["https://openalex.org/I153845743"]},{"raw_affiliation_string":"Moscow institute of physics and technology;","institution_ids":["https://openalex.org/I153845743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074503839","display_name":"D. V. Rastyagaev","orcid":"https://orcid.org/0000-0001-9465-6040","observed_orcids":["https://orcid.org/0000-0001-9465-6040","https://orcid.org/0000-0002-2071-8568"]},"institutions":[{"id":"https://openalex.org/I3129897247","display_name":"Russian New University","ror":"https://ror.org/00gj2kk32","country_code":"RU","type":"education","lineage":["https://openalex.org/I3129897247"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"D. V. Rastyagaev","raw_affiliation_strings":["Russian New University, Moscow, Russia","Russian New University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Russian New University, Moscow, Russia","institution_ids":["https://openalex.org/I3129897247"]},{"raw_affiliation_string":"Russian New University","institution_ids":["https://openalex.org/I3129897247"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6707,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.64006163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"16","issue":"2","first_page":"251","last_page":"264"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9609000086784363,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.9609000086784363,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.008700000122189522,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.005799999926239252,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/uniform-asymptotic-solution","display_name":"uniform asymptotic solution","score":0.8270000219345093},{"id":"https://openalex.org/keywords/catastrophe-theory","display_name":"catastrophe theory","score":0.8809999823570251},{"id":"https://openalex.org/keywords/wave-field","display_name":"wave field","score":0.7440000176429749},{"id":"https://openalex.org/keywords/special-functions","display_name":"special functions","score":0.7879999876022339},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"asymptotic expansion","score":0.8809999823570251}],"concepts":[{"id":"https://openalex.org/C33474566","wikidata":"https://www.wikidata.org/wiki/Q1345659","display_name":"Catastrophe theory","level":2,"score":0.6935627460479736},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6703895926475525},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6344234347343445},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.568547248840332},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.518743097782135},{"id":"https://openalex.org/C89407435","wikidata":"https://www.wikidata.org/wiki/Q17098224","display_name":"Method of matched asymptotic expansions","level":3,"score":0.507989227771759},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.48137906193733215},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.475960910320282},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4638313055038452},{"id":"https://openalex.org/C50757856","wikidata":"https://www.wikidata.org/wiki/Q867707","display_name":"Special functions","level":2,"score":0.43715041875839233},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.4273395538330078},{"id":"https://openalex.org/C3515459","wikidata":"https://www.wikidata.org/wiki/Q3140874","display_name":"Asymptotology","level":4,"score":0.41956204175949097},{"id":"https://openalex.org/C2779193601","wikidata":"https://www.wikidata.org/wiki/Q20026918","display_name":"Mathematical theory","level":2,"score":0.4116147756576538},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.403636634349823},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15655893087387085},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12315845489501953},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09402906894683838},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s1061920809020083","doi":"https://doi.org/10.1134/s1061920809020083","is_oa":false,"landing_page_url":"https://doi.org/10.1134/s1061920809020083","pdf_url":null,"source":{"id":"https://openalex.org/S121350373","display_name":"Russian Journal of Mathematical Physics","issn_l":"1061-9208","issn":["1061-9208","1555-6638"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Russian Journal of Mathematical Physics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1549037739","https://openalex.org/W1668186123","https://openalex.org/W1964928956","https://openalex.org/W1988230099","https://openalex.org/W2029770333","https://openalex.org/W2037261030","https://openalex.org/W2044987311","https://openalex.org/W2080177310","https://openalex.org/W2121303968","https://openalex.org/W2146034485","https://openalex.org/W2314729141","https://openalex.org/W2462037302","https://openalex.org/W2488538229","https://openalex.org/W2499350379","https://openalex.org/W2506656972","https://openalex.org/W2524023922","https://openalex.org/W2986873730","https://openalex.org/W3144205924","https://openalex.org/W4285719527","https://openalex.org/W4387673234"],"related_works":["https://openalex.org/W1964928956","https://openalex.org/W4407284228","https://openalex.org/W6999051662","https://openalex.org/W1972064856","https://openalex.org/W3022217632","https://openalex.org/W2560490047","https://openalex.org/W3117099497","https://openalex.org/W4392989688","https://openalex.org/W2026062660","https://openalex.org/W2069181957"],"abstract_inverted_index":{"A":[0],"mathematical":[1],"apparatus":[2],"for":[3],"solving":[4],"differential":[5],"equations":[6],"of":[7,13,23,35,44,54,57,61,70,80,86],"special":[8,62],"type":[9],"by":[10],"the":[11,24,31,42,55,58,78,84],"methods":[12,34,85],"main,":[14],"edge,":[15],"and":[16,33,83],"corner":[17],"catastrophes":[18],"is":[19],"developed.":[20],"The":[21],"fundamentals":[22],"wave":[25,45,71],"catastrophe":[26],"theory":[27],"are":[28,73],"considered,":[29],"including":[30],"classification":[32],"constructing":[36],"uniform":[37,67],"asymptotics":[38],"used":[39,64],"to":[40,65],"describe":[41],"structure":[43,56],"fields":[46,72],"in":[47],"these":[48,81],"domains,":[49],"together":[50,76],"with":[51,77],"an":[52],"analysis":[53],"field.":[59],"Classes":[60],"functions":[63],"construct":[66],"asymptotic":[68],"expansions":[69],"generally":[74],"described":[75],"properties":[79],"classes":[82],"computation.":[87]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2016-06-24T00:00:00"}
