{"id":"https://openalex.org/W4388262732","doi":"https://doi.org/10.1090/mcom/3922","title":"Long-time error bounds of low-regularity integrators for nonlinear Schr\u00f6dinger equations","display_name":"Long-time error bounds of low-regularity integrators for nonlinear Schr\u00f6dinger equations","publication_year":2023,"publication_date":"2023-10-25","ids":{"openalex":"https://openalex.org/W4388262732","doi":"https://doi.org/10.1090/mcom/3922"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3922","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3922","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":"article","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/A5100381176","display_name":"Yue Feng","orcid":"https://orcid.org/0009-0002-0771-7365"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Yue Feng","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00c3\u00a9, Paris 75005, France","LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00c3\u00a9, Paris 75005, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]},{"raw_affiliation_string":"LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081769352","display_name":"Georg Maierhofer","orcid":"https://orcid.org/0000-0002-9764-8596"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Georg Maierhofer","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00c3\u00a9, Paris 75005, France","LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00c3\u00a9, Paris 75005, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]},{"raw_affiliation_string":"LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027189972","display_name":"Katharina Schratz","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Katharina Schratz","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00c3\u00a9, Paris 75005, France","LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions, Sorbonne Universit\u00c3\u00a9, Paris 75005, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]},{"raw_affiliation_string":"LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions (Sorbonne-Universit\u00e9, Bo\u00eete courrier 187 - 75252 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100381176"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210158291"],"apc_list":null,"apc_paid":null,"fwci":3.7071,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.9430999,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"93","issue":"348","first_page":"1569","last_page":"1598"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9994999766349792,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6514780521392822},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44056516885757446},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3667914867401123}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6514780521392822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44056516885757446},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3667914867401123}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3922","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3922","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"},{"id":"pmh:oai:HAL:hal-04583125v1","is_oa":false,"landing_page_url":"https://u-paris.hal.science/hal-04583125","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.ams.org/journals/mcom/2024-93-348/S0025-5718-2023-03922-9/","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2314503370","display_name":null,"funder_award_id":"101064261","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":55,"referenced_works":["https://openalex.org/W31981613","https://openalex.org/W1542902041","https://openalex.org/W1606508258","https://openalex.org/W1816756658","https://openalex.org/W1866177120","https://openalex.org/W1973279410","https://openalex.org/W1977026647","https://openalex.org/W1988469123","https://openalex.org/W1989591635","https://openalex.org/W1997190030","https://openalex.org/W2027319347","https://openalex.org/W2031373684","https://openalex.org/W2033880071","https://openalex.org/W2035093985","https://openalex.org/W2039264003","https://openalex.org/W2050338742","https://openalex.org/W2056474482","https://openalex.org/W2063814247","https://openalex.org/W2075696551","https://openalex.org/W2093563917","https://openalex.org/W2117232282","https://openalex.org/W2117988589","https://openalex.org/W2119372460","https://openalex.org/W2136491192","https://openalex.org/W2182274314","https://openalex.org/W2275278987","https://openalex.org/W2512792594","https://openalex.org/W2528741806","https://openalex.org/W2565219097","https://openalex.org/W2618966431","https://openalex.org/W2917808692","https://openalex.org/W2947056241","https://openalex.org/W2964120365","https://openalex.org/W3023795180","https://openalex.org/W3036616071","https://openalex.org/W3039811077","https://openalex.org/W3101835573","https://openalex.org/W3159127758","https://openalex.org/W3163593804","https://openalex.org/W3174693435","https://openalex.org/W3203396613","https://openalex.org/W3212816381","https://openalex.org/W4200630032","https://openalex.org/W4211077197","https://openalex.org/W4224022239","https://openalex.org/W4226033512","https://openalex.org/W4245463005","https://openalex.org/W4247381331","https://openalex.org/W4256337705","https://openalex.org/W4286971439","https://openalex.org/W4288459455","https://openalex.org/W4310663747","https://openalex.org/W4389469254","https://openalex.org/W4390066194","https://openalex.org/W4402508920"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027"],"abstract_inverted_index":{"We":[0,86],"introduce":[1],"a":[2,68,193,282],"new":[3,208,271],"non-resonant":[4,209,272],"low-regularity":[5,57,90,196,214,273,293],"integrator":[6,91,197],"for":[7,15,59,92,269,295],"the":[8,23,26,38,43,52,60,89,93,98,104,153,184,199,203,218,226,231,254,257,262,270,278,296,305,311,316],"cubic":[9,204,297],"nonlinear":[10],"Schr\u00f6dinger":[11],"equation":[12],"(NLSE)":[13],"allowing":[14],"long-time":[16,46,187,200,279,317],"error":[17,47,53,188,227,265,280,306],"estimates":[18,307],"which":[19,97,216,275],"are":[20,267,301],"optimal":[21],"in":[22,36,96,198,315],"sense":[24],"of":[25,55,256],"underlying":[27],"partial":[28],"differential":[29],"equation.":[30],"The":[31],"main":[32],"idea":[33],"thereby":[34],"lies":[35],"treating":[37],"zeroth":[39,219],"mode":[40,220],"exactly":[41,102,221],"within":[42],"discretization.":[44],"For":[45,202],"estimates,":[48],"we":[49,206],"rigorously":[50,223],"establish":[51],"bounds":[54,266],"different":[56],"integrators":[58,215,294],"NLSE":[61,95],"with":[62,88,291,310],"small":[63],"initial":[64],"data":[65],"characterized":[66],"by":[67,281],"dimensionless":[69],"parameter<inline-formula":[70],"content-type=\"math/mathml\"><mml:math":[71,110,119,134,141,155,174,233,285],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[72,111,120,135,142,156,175,234,286],"alttext=\"epsilon":[73,287],"element-of":[74],"left-parenthesis":[75,123],"0":[76],"comma":[77],"1":[78,145],"right-bracket\"><mml:semantics><mml:mrow><mml:mi>\u03b5</mml:mi><mml:mo>\u2208</mml:mo><mml:mo":[79],"stretchy=\"false\">(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo":[80],"stretchy=\"false\">]</mml:mo></mml:mrow><mml:annotation":[81],"encoding=\"application/x-tex\">\\varepsilon":[82,289],"\\in":[83],"(0,":[84],"1]</mml:annotation></mml:semantics></mml:math></inline-formula>.":[85],"begin":[87],"quadratic":[94],"integral":[99],"is":[100,190],"computed":[101],"and":[103,211,222,308],"improved":[105,185,263],"uniform":[106,186,264],"first-order":[107,210],"convergence":[108],"in<inline-formula":[109,133],"alttext=\"upper":[112,121,136,157,176,235],"H":[113,137],"Superscript":[114,138],"r\"><mml:semantics><mml:msup><mml:mi>H</mml:mi><mml:mi>r</mml:mi></mml:msup><mml:annotation":[115,139],"encoding=\"application/x-tex\">H^r</mml:annotation></mml:semantics></mml:math></inline-formula>is":[116],"proven":[117],"at<inline-formula":[118],"O":[122],"epsilon":[124,160,238,244],"tau":[125],"right-parenthesis\"><mml:semantics><mml:mrow><mml:mi>O</mml:mi><mml:mo":[126],"stretchy=\"false\">(</mml:mo><mml:mi>\u03b5</mml:mi><mml:mi>\u03c4</mml:mi><mml:mo":[127],"stretchy=\"false\">)</mml:mo></mml:mrow><mml:annotation":[128],"encoding=\"application/x-tex\">O(\\varepsilon":[129],"\\tau":[130],")</mml:annotation></mml:semantics></mml:math></inline-formula>for":[131],"solutions":[132],"encoding=\"application/x-tex\">H^r</mml:annotation></mml:semantics></mml:math></inline-formula>with<inline-formula":[140],"alttext=\"r":[143],"greater-than":[144,178],"slash":[146,165,243],"2\"><mml:semantics><mml:mrow><mml:mi>r</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn><mml:mrow":[147],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:annotation":[148],"encoding=\"application/x-tex\">r":[149],"&gt;":[150,181],"1/2</mml:annotation></mml:semantics></mml:math></inline-formula>up":[151],"to":[152,192,230,303],"time<inline-formula":[154,232],"T":[158,164,177,236,242],"Subscript":[159,237],"Baseline":[161,239],"equals":[162,240],"upper":[163,241],"epsilon\"><mml:semantics><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow":[166],"class=\"MJX-TeXAtom-ORD\"><mml:mi>\u03b5</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mi>T</mml:mi><mml:mrow":[167,246],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:mi>\u03b5</mml:mi></mml:mrow><mml:annotation":[168],"encoding=\"application/x-tex\">T_{\\varepsilon":[169,248],"}":[170,249],"=":[171,250],"T/\\varepsilon</mml:annotation></mml:semantics></mml:math></inline-formula>with":[172],"fixed<inline-formula":[173],"0\"><mml:semantics><mml:mrow><mml:mi>T</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:annotation":[179],"encoding=\"application/x-tex\">T":[180],"0</mml:annotation></mml:semantics></mml:math></inline-formula>.":[182],"Then,":[183],"bound":[189],"extended":[191],"symmetric":[194,212],"second-order":[195,213],"regime.":[201],"NLSE,":[205],"design":[207],"treat":[217],"carry":[224],"out":[225],"analysis":[228],"up":[229],"squared\"><mml:semantics><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow":[245],"class=\"MJX-TeXAtom-ORD\"><mml:mo>/</mml:mo></mml:mrow><mml:msup><mml:mi>\u03b5</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:annotation":[247],"T/\\varepsilon":[251],"^2</mml:annotation></mml:semantics></mml:math></inline-formula>.":[252],"With":[253],"help":[255],"regularity":[258],"compensation":[259],"oscillation":[260],"technique,":[261],"established":[268],"schemes,":[274],"further":[276],"reduces":[277],"factor":[283],"of<inline-formula":[284],"squared\"><mml:semantics><mml:msup><mml:mi>\u03b5</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:annotation":[288],"^2</mml:annotation></mml:semantics></mml:math></inline-formula>compared":[290],"classical":[292,312],"NLSE.":[298],"Numerical":[299],"examples":[300],"presented":[302],"validate":[304],"compare":[309],"time-splitting":[313],"methods":[314],"simulations.":[318]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
