{"id":"https://openalex.org/W4390986594","doi":"https://doi.org/10.3390/sym16010115","title":"Noether Symmetry Analysis of the Klein\u2013Gordon and Wave Equations in Bianchi I Spacetime","display_name":"Noether Symmetry Analysis of the Klein\u2013Gordon and Wave Equations in Bianchi I Spacetime","publication_year":2024,"publication_date":"2024-01-18","ids":{"openalex":"https://openalex.org/W4390986594","doi":"https://doi.org/10.3390/sym16010115"},"language":"en","primary_location":{"id":"doi:10.3390/sym16010115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16010115","pdf_url":"https://www.mdpi.com/2073-8994/16/1/115/pdf?version=1705579632","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/1/115/pdf?version=1705579632","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067486825","display_name":"U\u011fur Camc\u0131","orcid":"https://orcid.org/0000-0003-3431-2574"},"institutions":[{"id":"https://openalex.org/I79839527","display_name":"Roger Williams University","ror":"https://ror.org/017nweb49","country_code":"US","type":"education","lineage":["https://openalex.org/I79839527"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ugur Camci","raw_affiliation_strings":["Department of Chemistry and Physics, Roger Williams University, One Old Ferry Road, Bristol, RI 02809, USA"],"affiliations":[{"raw_affiliation_string":"Department of Chemistry and Physics, Roger Williams University, One Old Ferry Road, Bristol, RI 02809, USA","institution_ids":["https://openalex.org/I79839527"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067486825"],"corresponding_institution_ids":["https://openalex.org/I79839527"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7148,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.82337992,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"16","issue":"1","first_page":"115","last_page":"115"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9997000098228455,"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":0.9997000098228455,"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":0.998199999332428,"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/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/noethers-theorem","display_name":"Noether's theorem","score":0.9682608842849731},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.833804726600647},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.8115160465240479},{"id":"https://openalex.org/keywords/spacetime-symmetries","display_name":"Spacetime symmetries","score":0.7430671453475952},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6662695407867432},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6550257205963135},{"id":"https://openalex.org/keywords/klein\u2013gordon-equation","display_name":"Klein\u2013Gordon equation","score":0.5624391436576843},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.5341628789901733},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.520327091217041},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.4745783805847168},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4222601056098938},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4196484088897705},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.18701186776161194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16390928626060486},{"id":"https://openalex.org/keywords/quantum-field-theory-in-curved-spacetime","display_name":"Quantum field theory in curved spacetime","score":0.14897167682647705},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09004488587379456},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06610807776451111},{"id":"https://openalex.org/keywords/quantum-gravity","display_name":"Quantum gravity","score":0.05175226926803589}],"concepts":[{"id":"https://openalex.org/C80892491","wikidata":"https://www.wikidata.org/wiki/Q578555","display_name":"Noether's theorem","level":3,"score":0.9682608842849731},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.833804726600647},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.8115160465240479},{"id":"https://openalex.org/C65305961","wikidata":"https://www.wikidata.org/wiki/Q7572737","display_name":"Spacetime symmetries","level":5,"score":0.7430671453475952},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6662695407867432},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6550257205963135},{"id":"https://openalex.org/C101682238","wikidata":"https://www.wikidata.org/wiki/Q868967","display_name":"Klein\u2013Gordon equation","level":3,"score":0.5624391436576843},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5341628789901733},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.520327091217041},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.4745783805847168},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4222601056098938},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4196484088897705},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.18701186776161194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16390928626060486},{"id":"https://openalex.org/C120484201","wikidata":"https://www.wikidata.org/wiki/Q2246697","display_name":"Quantum field theory in curved spacetime","level":4,"score":0.14897167682647705},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09004488587379456},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06610807776451111},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.05175226926803589},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym16010115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16010115","pdf_url":"https://www.mdpi.com/2073-8994/16/1/115/pdf?version=1705579632","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2401.11041","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2401.11041","pdf_url":"https://arxiv.org/pdf/2401.11041","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":null,"raw_type":"text"},{"id":"pmh:oai:docs.rwu.edu:fcas_fp-2055","is_oa":false,"landing_page_url":"https://docs.rwu.edu/fcas_fp/1046","pdf_url":null,"source":{"id":"https://openalex.org/S4377196758","display_name":"Roger Williams University - Digital Commons (Roger Williams University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79839527","host_organization_name":"Roger Williams University","host_organization_lineage":["https://openalex.org/I79839527"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Arts & Sciences Faculty Publications","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:9270a6fbfd9d40bcb508dd1346182c34","is_oa":true,"landing_page_url":"https://doaj.org/article/9270a6fbfd9d40bcb508dd1346182c34","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 1, p 115 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16010115","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16010115","pdf_url":"https://www.mdpi.com/2073-8994/16/1/115/pdf?version=1705579632","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life in Land","score":0.5799999833106995,"id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390986594.pdf","grobid_xml":"https://content.openalex.org/works/W4390986594.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W1445535793","https://openalex.org/W1698340928","https://openalex.org/W1824563381","https://openalex.org/W1953478438","https://openalex.org/W1996782992","https://openalex.org/W2013787451","https://openalex.org/W2036418683","https://openalex.org/W2042834821","https://openalex.org/W2045847998","https://openalex.org/W2053360550","https://openalex.org/W2059762690","https://openalex.org/W2060010976","https://openalex.org/W2062294311","https://openalex.org/W2062561585","https://openalex.org/W2062568658","https://openalex.org/W2066482999","https://openalex.org/W2069309832","https://openalex.org/W2075482579","https://openalex.org/W2083065506","https://openalex.org/W2086906649","https://openalex.org/W2158128318","https://openalex.org/W2261534158","https://openalex.org/W2298263218","https://openalex.org/W2411947368","https://openalex.org/W2532946548","https://openalex.org/W2624295710","https://openalex.org/W3101748718","https://openalex.org/W3102711049","https://openalex.org/W3103210655","https://openalex.org/W3105498094","https://openalex.org/W3124556707","https://openalex.org/W3154687133","https://openalex.org/W4211129695","https://openalex.org/W4211229636","https://openalex.org/W4214710653","https://openalex.org/W4256411646","https://openalex.org/W4292170110","https://openalex.org/W4317740369","https://openalex.org/W4387088000"],"related_works":["https://openalex.org/W2352103350","https://openalex.org/W158138185","https://openalex.org/W2122311148","https://openalex.org/W2002895720","https://openalex.org/W2105561882","https://openalex.org/W2802772034","https://openalex.org/W1978882646","https://openalex.org/W2162658570","https://openalex.org/W2321490767","https://openalex.org/W2144784797"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,6,25,35,48,51,61],"Noether":[3,21,44],"symmetries":[4],"of":[5,19,28,47],"Klein\u2013Gordon":[7,26,49],"Lagrangian":[8,27],"for":[9,24,54],"Bianchi":[10,29,55],"I":[11,30,56],"spacetime.":[12],"This":[13],"is":[14,58],"accomplished":[15],"using":[16],"a":[17,39],"set":[18],"new":[20],"symmetry":[22,45],"relations":[23],"spacetime,":[31],"which":[32],"reduces":[33],"to":[34],"wave":[36,52],"equation":[37],"in":[38],"special":[40],"case.":[41],"A":[42],"detailed":[43],"analysis":[46],"and":[50,60],"equations":[53],"spacetime":[57],"presented,":[59],"corresponding":[62],"conservation":[63],"laws":[64],"are":[65],"derived.":[66]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2024-01-19T00:00:00"}
