{"id":"https://openalex.org/W4415332134","doi":"https://doi.org/10.1137/25m1801633","title":"On the Rotating Nonlinear Klein\u2013Gordon Equation with Multiscale Effects: Structure-Preserving Methods and Applications to Vortex Dynamics","display_name":"On the Rotating Nonlinear Klein\u2013Gordon Equation with Multiscale Effects: Structure-Preserving Methods and Applications to Vortex Dynamics","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W4415332134","doi":"https://doi.org/10.1137/25m1801633"},"language":"en","primary_location":{"id":"doi:10.1137/25m1801633","doi":"https://doi.org/10.1137/25m1801633","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1801633","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.23191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Meng Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meng Li","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007391647","display_name":"Chunyan Niu","orcid":"https://orcid.org/0000-0001-8910-8373","observed_orcids":["https://orcid.org/0000-0001-8910-8373"]},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunyan Niu","raw_affiliation_strings":["Corresponding author. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Huifei Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I38877650","display_name":"Zhengzhou University","ror":"https://ror.org/04ypx8c21","country_code":"CN","type":"education","lineage":["https://openalex.org/I38877650"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huifei Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China","institution_ids":["https://openalex.org/I38877650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100607462","display_name":"Junjun Wang","orcid":"https://orcid.org/0000-0002-4669-8657","observed_orcids":["https://orcid.org/0000-0002-4669-8657"]},"institutions":[{"id":"https://openalex.org/I151878197","display_name":"Pingdingshan University","ror":"https://ror.org/026c29h90","country_code":"CN","type":"education","lineage":["https://openalex.org/I151878197"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junjun Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China","institution_ids":["https://openalex.org/I151878197"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01397429,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"4","first_page":"1595","last_page":"1634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7026000022888184,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.7026000022888184,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.21559999883174896,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.01720000058412552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiscale-problems","display_name":"multiscale problems","score":0.7039999961853027},{"id":"https://openalex.org/keywords/structure-preserving-numerical-methods","display_name":"structure-preserving numerical methods","score":0.7590000033378601},{"id":"https://openalex.org/keywords/galerkin-finite-element-method","display_name":"Galerkin finite element method","score":0.9729999899864197},{"id":"https://openalex.org/keywords/nonconforming-finite-elements","display_name":"nonconforming finite elements","score":0.8569999933242798},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7860000133514404},{"id":"https://openalex.org/keywords/vortex-dynamics","display_name":"vortex dynamics","score":0.878000020980835},{"id":"https://openalex.org/keywords/rotating-galaxies","display_name":"rotating galaxies","score":0.7260000109672546},{"id":"https://openalex.org/keywords/vortex-pair-interaction","display_name":"vortex pair interaction","score":0.6949999928474426},{"id":"https://openalex.org/keywords/bound-states","display_name":"bound states","score":0.7289999723434448}],"concepts":[{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.6470000147819519},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6338000297546387},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.616100013256073},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.531499981880188},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48660001158714294},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4562999904155731},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4287000000476837},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.3788999915122986},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.3644999861717224},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3481000065803528},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.33880001306533813},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.33169999718666077},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3176000118255615},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.3028999865055084},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.29280000925064087},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2736999988555908}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/25m1801633","doi":"https://doi.org/10.1137/25m1801633","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1801633","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2509.23191","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.23191","pdf_url":"https://arxiv.org/pdf/2509.23191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2509.23191","doi":"https://doi.org/10.48550/arxiv.2509.23191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.23191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2509.23191","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.23191","pdf_url":"https://arxiv.org/pdf/2509.23191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323845","display_name":"Natural Science Foundation of Henan Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415332134.pdf","grobid_xml":"https://content.openalex.org/works/W4415332134.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W585462275","https://openalex.org/W1576001493","https://openalex.org/W1927245093","https://openalex.org/W2001321113","https://openalex.org/W2006043132","https://openalex.org/W2015829426","https://openalex.org/W2027899421","https://openalex.org/W2033099995","https://openalex.org/W2039046666","https://openalex.org/W2050066690","https://openalex.org/W2050338742","https://openalex.org/W2058992888","https://openalex.org/W2061904552","https://openalex.org/W2065469285","https://openalex.org/W2066944044","https://openalex.org/W2071438440","https://openalex.org/W2099597895","https://openalex.org/W2101011779","https://openalex.org/W2240299529","https://openalex.org/W2255687522","https://openalex.org/W2467378457","https://openalex.org/W2480237505","https://openalex.org/W2524595001","https://openalex.org/W2662118020","https://openalex.org/W2927547302","https://openalex.org/W2953424886","https://openalex.org/W3127420056","https://openalex.org/W3128956670","https://openalex.org/W3204708751","https://openalex.org/W4231909063","https://openalex.org/W4232654152","https://openalex.org/W4246447829","https://openalex.org/W4388459427","https://openalex.org/W4402850253","https://openalex.org/W4406977865"],"related_works":["https://openalex.org/W2927547302","https://openalex.org/W4402185375","https://openalex.org/W4406977865","https://openalex.org/W7170190430","https://openalex.org/W4280533281","https://openalex.org/W2896857931","https://openalex.org/W3013627705","https://openalex.org/W4398170705","https://openalex.org/W4412704048","https://openalex.org/W4200014372"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"study":[2],"numerical":[3,137],"methods":[4,72],"for":[5,74],"the":[6,27,43,62,75,83,141,147,157,160],"rotating":[7,40],"nonlinear":[8],"Klein\u2013Gordon":[9],"(RKG)":[10],"equation,":[11],"a":[12,30,98,103,117],"fundamental":[13],"model":[14],"in":[15],"relativistic":[16,158,169],"quantum":[17],"physics,":[18],"which":[19,139],"exhibits":[20],"highly":[21],"oscillatory":[22],"multiscale":[23],"behavior":[24],"due":[25],"to":[26,108,159,165],"presence":[28],"of":[29,52,67,146,152,176],"small":[31],"parameter":[32],"[Formula:":[33],"see":[34],"text].":[35],"The":[36],"RKG":[37,76],"equation":[38],"models":[39],"galaxies":[41],"under":[42],"Minkowski":[44],"metric":[45],"and":[46,64,94,111,124,144,174],"also":[47],"provides":[48],"an":[49],"effective":[50],"description":[51],"phenomena":[53],"such":[54],"as":[55],"cosmic":[56],"superfluids.":[57],"This":[58],"work":[59],"focuses":[60],"on":[61,171],"development":[63],"rigorous":[65],"analysis":[66],"structure-preserving":[68,105,148],"Galerkin":[69],"finite":[70],"element":[71],"(FEMs)":[73],"equation.":[77],"A":[78],"central":[79],"challenge":[80],"is":[81],"that":[82],"rotational":[84],"terms":[85],"prevent":[86],"traditional":[87],"nonconforming":[88,112],"FEMs":[89],"from":[90,156],"simultaneously":[91],"conserving":[92],"energy":[93],"charge.":[95],"By":[96],"employing":[97],"conservation-adjusting":[99],"technique,":[100],"we":[101,115],"construct":[102],"consistent":[104],"algorithm":[106],"applicable":[107],"both":[109],"conforming":[110],"FEMs.":[113],"Moreover,":[114],"provide":[116],"comprehensive":[118],"convergence":[119],"analysis,":[120],"establishing":[121],"unconditional":[122],"optimal":[123],"high-order":[125],"accuracy":[126],"error":[127],"estimates.":[128],"These":[129],"theoretical":[130],"results":[131],"are":[132,163],"further":[133],"validated":[134],"through":[135],"extensive":[136],"experiments,":[138],"demonstrate":[140],"accuracy,":[142],"efficiency,":[143],"robustness":[145],"schemes.":[149],"Finally,":[150],"simulations":[151],"vortex":[153,167,177],"dynamics,":[154],"ranging":[155],"nonrelativistic":[161],"regimes,":[162],"presented":[164],"illustrate":[166],"creation,":[168],"effects":[170],"bound":[172],"states,":[173],"interactions":[175],"pairs.":[178]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-19T00:00:00"}