{"id":"https://openalex.org/W3172321500","doi":"https://doi.org/10.3390/sym13061022","title":"Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov\u2013Kuznetsov Equation in Quantum Magneto-Plasmas","display_name":"Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov\u2013Kuznetsov Equation in Quantum Magneto-Plasmas","publication_year":2021,"publication_date":"2021-06-07","ids":{"openalex":"https://openalex.org/W3172321500","doi":"https://doi.org/10.3390/sym13061022","mag":"3172321500"},"language":"en","primary_location":{"id":"doi:10.3390/sym13061022","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061022","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1022/pdf","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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/6/1022/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110557738","display_name":"Yan-Hong Liang","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]},{"id":"https://openalex.org/I4210109718","display_name":"Shandong Transportation Research Institute","ror":"https://ror.org/01wcts620","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210109718"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan-Hong Liang","raw_affiliation_strings":["School of Qilu Transportation, Shandong University, Jinan 250061, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Qilu Transportation, Shandong University, Jinan 250061, China","institution_ids":["https://openalex.org/I4210109718","https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064814377","display_name":"Kang\u2010Jia Wang","orcid":"https://orcid.org/0000-0002-3905-0844"},"institutions":[{"id":"https://openalex.org/I4210166499","display_name":"Henan Polytechnic University","ror":"https://ror.org/05vr1c885","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210166499"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Kang-Jia Wang","raw_affiliation_strings":["School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"],"raw_orcid":"https://orcid.org/0000-0002-3905-0844","affiliations":[{"raw_affiliation_string":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China","institution_ids":["https://openalex.org/I4210166499"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064814377"],"corresponding_institution_ids":["https://openalex.org/I4210166499"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5127,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63433983,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"13","issue":"6","first_page":"1022","last_page":"1022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.989300012588501,"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/fractal","display_name":"Fractal","score":0.8892692923545837},{"id":"https://openalex.org/keywords/fractal-derivative","display_name":"Fractal derivative","score":0.6988170146942139},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.6930245161056519},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.5274122953414917},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.46499741077423096},{"id":"https://openalex.org/keywords/magneto","display_name":"Magneto","score":0.419220894575119},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4166930317878723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4142364263534546},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.41396594047546387},{"id":"https://openalex.org/keywords/fractal-dimension","display_name":"Fractal dimension","score":0.35909390449523926},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.35836225748062134},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3405749201774597},{"id":"https://openalex.org/keywords/fractal-analysis","display_name":"Fractal analysis","score":0.2197255790233612},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16121318936347961},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10884684324264526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1024756133556366}],"concepts":[{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.8892692923545837},{"id":"https://openalex.org/C83764196","wikidata":"https://www.wikidata.org/wiki/Q17014577","display_name":"Fractal derivative","level":5,"score":0.6988170146942139},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.6930245161056519},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5274122953414917},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46499741077423096},{"id":"https://openalex.org/C171636128","wikidata":"https://www.wikidata.org/wiki/Q1307177","display_name":"Magneto","level":3,"score":0.419220894575119},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4166930317878723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4142364263534546},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.41396594047546387},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.35909390449523926},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.35836225748062134},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3405749201774597},{"id":"https://openalex.org/C162494671","wikidata":"https://www.wikidata.org/wiki/Q2845227","display_name":"Fractal analysis","level":4,"score":0.2197255790233612},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16121318936347961},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10884684324264526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1024756133556366},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13061022","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061022","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1022/pdf","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:doaj.org/article:de9c83eb7ca84f10bcbe28d91d7d9c95","is_oa":true,"landing_page_url":"https://doaj.org/article/de9c83eb7ca84f10bcbe28d91d7d9c95","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 6, p 1022 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/6/1022/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13061022","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13061022","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13061022","pdf_url":"https://www.mdpi.com/2073-8994/13/6/1022/pdf","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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3172321500.pdf"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W2012676400","https://openalex.org/W2014086804","https://openalex.org/W2039978815","https://openalex.org/W2060356946","https://openalex.org/W2066884096","https://openalex.org/W2072709917","https://openalex.org/W2081454935","https://openalex.org/W2084154755","https://openalex.org/W2087535766","https://openalex.org/W2141858378","https://openalex.org/W2150545288","https://openalex.org/W2514133828","https://openalex.org/W2606708326","https://openalex.org/W2793390268","https://openalex.org/W2806796560","https://openalex.org/W2807734377","https://openalex.org/W2919736785","https://openalex.org/W2964033105","https://openalex.org/W2966767785","https://openalex.org/W2970965816","https://openalex.org/W2979892876","https://openalex.org/W2983577480","https://openalex.org/W2992551182","https://openalex.org/W2994893055","https://openalex.org/W3001671786","https://openalex.org/W3005468129","https://openalex.org/W3008882901","https://openalex.org/W3011459722","https://openalex.org/W3016442179","https://openalex.org/W3040760886","https://openalex.org/W3043358877","https://openalex.org/W3083782183","https://openalex.org/W3084288022","https://openalex.org/W3086186633","https://openalex.org/W3090205946","https://openalex.org/W3095351266","https://openalex.org/W3097417748","https://openalex.org/W3097934281","https://openalex.org/W3106820458","https://openalex.org/W3109230970","https://openalex.org/W3110144190","https://openalex.org/W3113233544","https://openalex.org/W3116630743","https://openalex.org/W3119186313","https://openalex.org/W3125019829","https://openalex.org/W3131877146","https://openalex.org/W3135073731","https://openalex.org/W3135362462","https://openalex.org/W3135396605","https://openalex.org/W3137819205","https://openalex.org/W3161869913","https://openalex.org/W3163120565","https://openalex.org/W3164061889","https://openalex.org/W3164392138","https://openalex.org/W6670806266","https://openalex.org/W6682000055","https://openalex.org/W6768956794","https://openalex.org/W6776326146","https://openalex.org/W6795851663"],"related_works":["https://openalex.org/W4308571620","https://openalex.org/W2394117909","https://openalex.org/W2896054214","https://openalex.org/W2017118246","https://openalex.org/W4391810631","https://openalex.org/W4386695727","https://openalex.org/W2972268228","https://openalex.org/W4308570214","https://openalex.org/W2352533455","https://openalex.org/W2355197944"],"abstract_inverted_index":{"In":[0],"this":[1,67],"paper,":[2],"we":[3],"propose":[4],"the":[5,18,30,49,52,61,72,77],"fractal":[6,15,22,35,39,78],"(2":[7],"+":[8],"1)-dimensional":[9],"Zakharov\u2013Kuznetsov":[10],"equation":[11],"based":[12],"on":[13],"He\u2019s":[14],"derivative":[16],"for":[17],"first":[19],"time.":[20],"The":[21,37,64],"generalized":[23],"variational":[24,40],"formulation":[25],"is":[26,42],"established":[27],"by":[28],"using":[29],"semi-inverse":[31],"method":[32],"and":[33],"two-scale":[34],"theory.":[36,63],"obtained":[38],"principle":[41],"important":[43],"since":[44],"it":[45],"not":[46],"only":[47],"reveals":[48],"structure":[50],"of":[51,66,74],"traveling":[53],"wave":[54],"solutions":[55],"but":[56],"also":[57],"helps":[58],"us":[59],"study":[60,73],"symmetric":[62],"finding":[65],"paper":[68],"will":[69],"contribute":[70],"to":[71],"symmetry":[75],"in":[76],"space.":[79]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
