{"id":"https://openalex.org/W4406418605","doi":"https://doi.org/10.1090/mcom/4070","title":"Low regularity estimates of the Lie-Trotter time-splitting Fourier spectral method for the logarithmic Schr\u00f6dinger equation","display_name":"Low regularity estimates of the Lie-Trotter time-splitting Fourier spectral method for the logarithmic Schr\u00f6dinger equation","publication_year":2025,"publication_date":"2025-01-15","ids":{"openalex":"https://openalex.org/W4406418605","doi":"https://doi.org/10.1090/mcom/4070"},"language":"lv","primary_location":{"id":"doi:10.1090/mcom/4070","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4070","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027722546","display_name":"Xiaolong Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaolong Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5112395743","display_name":"Li-Lian Wang","orcid":"https://orcid.org/0000-0002-2735-9019"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li-Lian Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"95","issue":"358","first_page":"773","last_page":"801"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9580000042915344,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9580000042915344,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9505000114440918,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9429000020027161,"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/logarithm","display_name":"Logarithm","score":0.6412413716316223},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5722634196281433},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5168207287788391},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47167500853538513},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37650740146636963},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.344826877117157}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6412413716316223},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5722634196281433},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5168207287788391},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47167500853538513},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37650740146636963},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.344826877117157}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/4070","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/4070","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1531371725","https://openalex.org/W1964470050","https://openalex.org/W1993142553","https://openalex.org/W2013432148","https://openalex.org/W2020107848","https://openalex.org/W2071357402","https://openalex.org/W2076523251","https://openalex.org/W2088629022","https://openalex.org/W2111755943","https://openalex.org/W2169053604","https://openalex.org/W2171594451","https://openalex.org/W2198522932","https://openalex.org/W2312961750","https://openalex.org/W2563583896","https://openalex.org/W2618966431","https://openalex.org/W2795033786","https://openalex.org/W2902944228","https://openalex.org/W3036616071","https://openalex.org/W3165482041","https://openalex.org/W3186094127","https://openalex.org/W3210061315","https://openalex.org/W3212454870","https://openalex.org/W4221156494","https://openalex.org/W4225769618","https://openalex.org/W4253937035","https://openalex.org/W4283315155","https://openalex.org/W4315588542","https://openalex.org/W4321472157","https://openalex.org/W4363632305","https://openalex.org/W4382618459","https://openalex.org/W4396779037","https://openalex.org/W4400018653","https://openalex.org/W4403055316"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,95],"conduct":[4],"rigorous":[5],"error":[6],"analysis":[7],"of":[8,61,120],"the":[9,16,62,98,101,113,116,121],"Lie-Trotter":[10],"time-splitting":[11,114],"Fourier":[12],"spectral":[13],"scheme":[14],"for":[15],"nonlinear":[17,23,63,122],"Schr\u00f6dinger":[18],"equation":[19],"with":[20,100],"a":[21,44,148],"logarithmic":[22],"term":[24,64],"f":[25,65,70,103,152],"(":[26,66,72,79,104,125,153],"u":[27,30,33,67,73,76,81,126,129,137],")":[28,68,74,85,106,127],"=":[29,75,107,128],"ln":[31,77,135],"|":[32,34,80,82,136,138],"2":[35,86,139],"f(u)=u\\ln":[36],"\\!|u|^2":[37],"(LogSE)":[38],"and":[39],"periodic":[40],"boundary":[41],"conditions":[42],"on":[43,59],"d":[45,46,50],"-dimensional":[47],"torus":[48],"T":[49],"\\mathbb":[51],"{T}^d":[52],".":[53,110],"Different":[54],"from":[55],"existing":[56],"works":[57],"based":[58],"regularisation":[60],"\u2248":[69],"\u03b5":[71,84],"\u2061":[78],"+":[83,91],"f(u)\\approx":[87],"f^\\varepsilon":[88],"(u)=u\\ln":[89],"(|u|":[90],"\\varepsilon":[92],")^2":[93],",":[94],"directly":[96],"discretize":[97],"LogSE":[99],"understanding":[102],"0":[105,108],"f(0)=0":[109],"Remarkably,":[111],"in":[112],"scheme,":[115],"solution":[117],"flow":[118],"map":[119],"part:":[123],"g":[124],"e":[130],"\u2212":[131],"i":[132],"\u03bb":[133],"t":[134,144],"g(u)=":[140],"u\\,e^{-{\\mathrm":[141],"{i}}":[142],"\\lambda":[143],"\\ln":[145],"\\!|u|^{2}}":[146],"has":[147],"higher":[149],"regularity":[150],"than":[151]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-01-16T00:00:00"}