{"id":"https://openalex.org/W2995698153","doi":"https://doi.org/10.15407/ujpe64.12.1103","title":"On the Classification of Symmetry Reductions and Invariant Solutions for the Euler\u2013Lagrange\u2013Born\u2013Infeld Equation","display_name":"On the Classification of Symmetry Reductions and Invariant Solutions for the Euler\u2013Lagrange\u2013Born\u2013Infeld Equation","publication_year":2019,"publication_date":"2019-12-09","ids":{"openalex":"https://openalex.org/W2995698153","doi":"https://doi.org/10.15407/ujpe64.12.1103","mag":"2995698153"},"language":"en","primary_location":{"id":"doi:10.15407/ujpe64.12.1103","doi":"https://doi.org/10.15407/ujpe64.12.1103","is_oa":true,"landing_page_url":"https://doi.org/10.15407/ujpe64.12.1103","pdf_url":"https://ujp.bitp.kiev.ua/index.php/ujp/article/download/2019539/1518","source":{"id":"https://openalex.org/S115306628","display_name":"Ukrainian Journal of Physics","issn_l":"2071-0186","issn":["2071-0186","2071-0194"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310321651","host_organization_name":"Naukova Dumka","host_organization_lineage":["https://openalex.org/P4310321651"],"host_organization_lineage_names":["Naukova Dumka"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ukrainian Journal of Physics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://ujp.bitp.kiev.ua/index.php/ujp/article/download/2019539/1518","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046062047","display_name":"Vasyl M. Fedorchuk","orcid":"https://orcid.org/0000-0003-0164-2673","observed_orcids":["https://orcid.org/0000-0003-0164-2673"]},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I4210145787","display_name":"Pidstryhach Institute for Applied Problems of Mechanics and Mathematics","ror":"https://ror.org/05dry3213","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"V. M. Fedorchuk","raw_affiliation_strings":["Institute of Mathematics, Pedagogical University, Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine","Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Pedagogical University, Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine","institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]},{"raw_affiliation_string":"Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine","institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102995957","display_name":"Volodymyr I. Fedorchuk","orcid":"https://orcid.org/0000-0002-5248-7776","observed_orcids":["https://orcid.org/0000-0002-5248-7776","https://orcid.org/0000-0002-3540-0237"]},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I4210145787","display_name":"Pidstryhach Institute for Applied Problems of Mechanics and Mathematics","ror":"https://ror.org/05dry3213","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"V. I. Fedorchuk","raw_affiliation_strings":["Institute of Mathematics, Pedagogical University, Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine","Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Pedagogical University, Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine","institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]},{"raw_affiliation_string":"Ya.S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Nat. Acad. of Sci. of Ukraine","institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210145787"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3078,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.4355877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":95},"biblio":{"volume":"64","issue":"12","first_page":"1103","last_page":"1103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.614300012588501,"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":0.614300012588501,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.3190999925136566,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11960","display_name":"Relativity and Gravitational Theory","score":0.027499999850988388,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"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/symmetry-lowering","display_name":"symmetry reduction","score":0.8619999885559082},{"id":"https://openalex.org/keywords/invariant-solutions","display_name":"invariant solutions","score":0.9909999966621399},{"id":"https://openalex.org/keywords/classification-of-subalgebras","display_name":"classification of subalgebras","score":0.6549999713897705}],"concepts":[{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6980350613594055},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5937284231185913},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5741161108016968},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.531263530254364},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.5092614889144897},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5025997161865234},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.47509849071502686},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4613701105117798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4305611848831177},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4229316711425781},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.42179858684539795},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35363003611564636},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.061857521533966064}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.15407/ujpe64.12.1103","doi":"https://doi.org/10.15407/ujpe64.12.1103","is_oa":true,"landing_page_url":"https://doi.org/10.15407/ujpe64.12.1103","pdf_url":"https://ujp.bitp.kiev.ua/index.php/ujp/article/download/2019539/1518","source":{"id":"https://openalex.org/S115306628","display_name":"Ukrainian Journal of Physics","issn_l":"2071-0186","issn":["2071-0186","2071-0194"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310321651","host_organization_name":"Naukova Dumka","host_organization_lineage":["https://openalex.org/P4310321651"],"host_organization_lineage_names":["Naukova Dumka"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ukrainian Journal of Physics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.15407/ujpe64.12.1103","doi":"https://doi.org/10.15407/ujpe64.12.1103","is_oa":true,"landing_page_url":"https://doi.org/10.15407/ujpe64.12.1103","pdf_url":"https://ujp.bitp.kiev.ua/index.php/ujp/article/download/2019539/1518","source":{"id":"https://openalex.org/S115306628","display_name":"Ukrainian Journal of Physics","issn_l":"2071-0186","issn":["2071-0186","2071-0194"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310321651","host_organization_name":"Naukova Dumka","host_organization_lineage":["https://openalex.org/P4310321651"],"host_organization_lineage_names":["Naukova Dumka"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ukrainian Journal of Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2995698153.pdf","grobid_xml":"https://content.openalex.org/works/W2995698153.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1981116812","https://openalex.org/W2003576097","https://openalex.org/W2007771320","https://openalex.org/W2020213966","https://openalex.org/W2039117838","https://openalex.org/W2056109643","https://openalex.org/W2077526843","https://openalex.org/W2149557743","https://openalex.org/W2156047387","https://openalex.org/W2427148153","https://openalex.org/W2779819049","https://openalex.org/W2783350103","https://openalex.org/W2963331388","https://openalex.org/W3003584233","https://openalex.org/W3022230513","https://openalex.org/W4206617088","https://openalex.org/W4229672964","https://openalex.org/W4251151584"],"related_works":["https://openalex.org/W3085431863","https://openalex.org/W2156047387","https://openalex.org/W2783350103","https://openalex.org/W2427148153","https://openalex.org/W7161638385","https://openalex.org/W147160138","https://openalex.org/W2111217629","https://openalex.org/W4413061820","https://openalex.org/W3087509094","https://openalex.org/W402988795"],"abstract_inverted_index":{"We":[0,36],"study":[1],"a":[2],"connection":[3],"between":[4],"the":[5,9,17,21,27,33,39,45,61,65,73,82],"structural":[6],"properties":[7],"of":[8,16,20,29,41,60,64,75,81],"low-dimension":[10],"(dimL":[11],"\u2264":[12],"3)":[13],"nonconjugate":[14,58],"subalgebras":[15,59],"Lie":[18,62],"argebra":[19],"generalized":[22],"Poincar\u00b4e":[23],"group":[24,66],"P(1,4)":[25],"and":[26,78],"results":[28,69],"symmetry":[30,76],"reductions":[31,77],"for":[32,72],"Euler\u2013Lagrange\u2013Born\u2013Infeld":[34,83],"equation.":[35,84],"have":[37],"performed":[38],"classification":[40,74],"nonsingular":[42],"manifolds":[43],"in":[44],"space":[46],"M(1":[47],",":[48],"3":[49],")":[50],"\u00d7":[51],"R(u)":[52],"invariant":[53,79],"with":[54],"respect":[55],"to":[56],"three-dimensional":[57],"algebra":[63],"P(1,4).":[67],"The":[68],"are":[70],"used":[71],"solutions":[80]},"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":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-10-01T08:54:57.152042","created_date":"2019-12-26T00:00:00"}
