{"id":"https://openalex.org/W7134055492","doi":"https://doi.org/10.48550/arxiv.2603.04984","title":"$\\mathrm{L}^{2}$--convergence of the time-splitting scheme for nonlinear Dirac equation in 1+1 dimensions","display_name":"$\\mathrm{L}^{2}$--convergence of the time-splitting scheme for nonlinear Dirac equation in 1+1 dimensions","publication_year":2026,"publication_date":"2026-03-05","ids":{"openalex":"https://openalex.org/W7134055492","doi":"https://doi.org/10.48550/arxiv.2603.04984"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2603.04984","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089616336","display_name":"N. Li","orcid":"https://orcid.org/0000-0002-3682-8753"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Ningning","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128259305","display_name":"Yongqian Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Yongqian","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128222378","display_name":"Qin Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Qin","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089616336"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9672999978065491,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9672999978065491,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.008799999952316284,"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"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.0024999999441206455,"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/subsequence","display_name":"Subsequence","score":0.6699000000953674},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6223999857902527},{"id":"https://openalex.org/keywords/dirac-measure","display_name":"Dirac measure","score":0.565500020980835},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.5630999803543091},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5268999934196472},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.522599995136261},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5048999786376953},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4449000060558319}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7325000166893005},{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.6699000000953674},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6223999857902527},{"id":"https://openalex.org/C111118313","wikidata":"https://www.wikidata.org/wiki/Q1227387","display_name":"Dirac measure","level":5,"score":0.565500020980835},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5630999803543091},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5314000248908997},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5268999934196472},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.522599995136261},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4449000060558319},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.41190001368522644},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.4032000005245209},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.39419999718666077},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.3050999939441681},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29330000281333923},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.28600001335144043},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.26820001006126404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2603.04984","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2603.04984","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.04984","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2603.04984","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,9,13,21,24,28,37,42,52,57,67,99,105,121,127,131,136,140],"time-splitting":[3,44,71,108,128],"scheme":[4,29,45],"for":[5,27,70,98,114],"approximating":[6],"solutions":[7,39,109,129],"to":[8,51,84,135],"Cauchy":[10,137],"problem":[11,138],"of":[12,56,107,123,126,139],"nonlinear":[14,58,141],"Dirac":[15,59,142],"equation":[16],"in":[17,32,49,91,112],"1+1":[18],"dimensions.":[19],"Under":[20],"assumption":[22],"that":[23,36,86,104,120],"initial":[25],"data":[26],"are":[30,46],"convergent":[31,48],"$\\mathrm{L}^{2}(\\mathbb{R})$,":[33],"we":[34,64,102,118],"prove":[35,103],"approximate":[38],"constructed":[40],"by":[41],"corresponding":[43],"strongly":[47],"$\\mathrm{C}([0,\\infty);\\mathrm{L}^{2}(\\mathbb{R}))$":[50],"global":[53],"strong":[54,133],"solution":[55,134],"equation.":[60,143],"To":[61],"achieve":[62],"this,":[63],"first":[65],"establish":[66],"pointwise":[68],"estimates":[69,97],"solutions.":[72],"Based":[73],"on":[74],"these":[75],"estimates,":[76],"a":[77],"modified":[78],"Glimm-type":[79],"functional":[80],"is":[81,88,110,130],"carefully":[82],"designed":[83],"show":[85,119],"it":[87],"uniformly":[89],"bounded":[90],"time,":[92],"which":[93],"yields":[94],"$\\mathrm{L}^2$":[95],"stability":[96],"scheme.":[100],"Furthermore,":[101],"set":[106],"precompact":[111],"$\\mathrm{C}([0,T];\\mathrm{L}^{2}(\\mathbb{R}))$":[113],"any":[115,124],"$T&gt;0$.":[116],"Finally,":[117],"limit":[122],"subsequence":[125],"unique":[132]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2026-03-07T00:00:00"}
