{"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":false,"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)"],"raw_orcid":null,"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)"],"raw_orcid":null,"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)"],"raw_orcid":null,"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":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.6331,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.94162826,"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/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"info:eu-repo/semantics/article"}],"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"},{"id":"https://openalex.org/G3392671992","display_name":null,"funder_award_id":"101064261","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"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":[0,107],"introduce":[1],"a":[2,68,313,431],"new":[3,328,420],"non-resonant":[4,329,421],"low-regularity":[5,57,111,316,334,422,456],"integrator":[6,112,317],"for":[7,15,59,113,183,418,458],"the":[8,23,26,38,43,52,60,110,114,119,125,234,304,319,323,338,346,351,403,406,411,419,427,459,468,474,479],"cubic":[9,324,460],"nonlinear":[10],"Schr\u00f6dinger":[11],"equation":[12],"(NLSE)":[13],"allowing":[14],"long-time":[16,46,307,320,428],"error":[17,47,53,308,347,414,429,469],"estimates":[18,470],"which":[19,118,336,424],"are":[20,416,464],"optimal":[21],"in":[22,36,117,130,185,318,478],"sense":[24],"of":[25,55,405,433],"underlying":[27],"partial":[28],"differential":[29],"equation.":[30],"The":[31],"main":[32],"idea":[33],"thereby":[34],"lies":[35],"treating":[37],"zeroth":[39,339],"mode":[40,340],"exactly":[41,123,341],"within":[42],"discretization.":[44],"For":[45,322],"estimates,":[48],"we":[49,326],"rigorously":[50,343],"establish":[51],"bounds":[54,415],"different":[56],"integrators":[58,335,457],"NLSE":[61,116],"with":[62,109,204,279,454,473],"small":[63],"initial":[64],"data":[65],"characterized":[66],"by":[67,430],"dimensionless":[69],"parameter":[70],"<inline-formula":[71,131,152,186,205,236,281,353,434],"content-type=\"math/mathml\">":[72,132,153,187,206,237,282,354,435],"<mml:math":[73,133,154,188,207,238,283,355,436],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[74,134,155,189,208,239,284,356,437],"alttext=\"epsilon":[75,438],"element-of":[76],"left-parenthesis":[77,158],"0":[78],"comma":[79],"1":[80,211],"right-bracket\">":[81],"<mml:semantics>":[82,139,162,194,214,250,289,368,440],"<mml:mrow>":[83,163,215,251,290,369],"<mml:mi>":[84,167,170,256,267,374,386,442],"\u03b5":[85,168,257,268,375,387,443],"</mml:mi>":[86,169,172,258,269,376,388,444],"<mml:mo>":[87],"\u2208":[88],"</mml:mo>":[89],"<mml:mo":[90,95,165,173],"stretchy=\"false\">(</mml:mo>":[91,166],"<mml:mn>0</mml:mn>":[92,293],"<mml:mo>,</mml:mo>":[93],"<mml:mn>1</mml:mn>":[94,218],"stretchy=\"false\">]</mml:mo>":[96],"</mml:mrow>":[97,175,222,224,259,266,270,294,377,384,391],"<mml:annotation":[98,144,176,199,225,271,295,392,447],"encoding=\"application/x-tex\">\\varepsilon":[99,448],"\\in":[100],"(0,":[101],"1]</mml:annotation>":[102],"</mml:semantics>":[103,146,180,201,229,276,299,398,450],"</mml:math>":[104,147,181,202,230,277,300,399,451],"</inline-formula>":[105,148,182,203,231,278,301,400,452],".":[106,302,401],"begin":[108],"quadratic":[115],"integral":[120],"is":[121,149,310],"computed":[122],"and":[124,331,342,471],"improved":[126,305,412],"uniform":[127,306,413],"first-order":[128,330],"convergence":[129],"alttext=\"upper":[135,156,190,240,285,357],"H":[136,191],"Superscript":[137,192],"r\">":[138,193],"<mml:msup>":[140,195,385,441],"<mml:mi>H</mml:mi>":[141,196],"<mml:mi>r</mml:mi>":[142,197,216],"</mml:msup>":[143,198,390,446],"encoding=\"application/x-tex\">H^r</mml:annotation>":[145,200],"proven":[150],"at":[151],"O":[157],"epsilon":[159,243,360,366],"tau":[160],"right-parenthesis\">":[161],"<mml:mi>O</mml:mi>":[164],"\u03c4":[171],"stretchy=\"false\">)</mml:mo>":[174],"encoding=\"application/x-tex\">O(\\varepsilon":[177],"\\tau":[178],")</mml:annotation>":[179],"solutions":[184],"alttext=\"r":[209],"greater-than":[210,287],"slash":[212,248,365],"2\">":[213],"<mml:mo>&gt;</mml:mo>":[217,292],"<mml:mrow":[219,254,263,372,381],"class=\"MJX-TeXAtom-ORD\">":[220,255,264,373,382],"<mml:mo>/</mml:mo>":[221,265,383],"<mml:mn>2</mml:mn>":[223,389,445],"encoding=\"application/x-tex\">r":[226],"&gt;":[227,297],"1/2</mml:annotation>":[228],"up":[232,349],"to":[233,312,350,466],"time":[235,352],"T":[241,247,286,358,364],"Subscript":[242,359],"Baseline":[244,361],"equals":[245,362],"upper":[246,363],"epsilon\">":[249],"<mml:msub>":[252,370],"<mml:mi>T</mml:mi>":[253,262,291,371,380],"</mml:msub>":[260,378],"<mml:mo>=</mml:mo>":[261,379],"encoding=\"application/x-tex\">T_{\\varepsilon":[272,393],"}":[273,394],"=":[274,395],"T/\\varepsilon</mml:annotation>":[275],"fixed":[280],"0\">":[288],"encoding=\"application/x-tex\">T":[296],"0</mml:annotation>":[298],"Then,":[303],"bound":[309],"extended":[311],"symmetric":[314,332],"second-order":[315,333],"regime.":[321],"NLSE,":[325],"design":[327],"treat":[337],"carry":[344],"out":[345],"analysis":[348],"squared\">":[367,439],"T/\\varepsilon":[396],"^2</mml:annotation>":[397,449],"With":[402],"help":[404],"regularity":[407],"compensation":[408],"oscillation":[409],"technique,":[410],"established":[417],"schemes,":[423],"further":[425],"reduces":[426],"factor":[432],"compared":[453],"classical":[455,475],"NLSE.":[461],"Numerical":[462],"examples":[463],"presented":[465],"validate":[467],"compare":[472],"time-splitting":[476],"methods":[477],"long-":[480]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-13T07:31:44.756512","created_date":"2025-10-10T00:00:00"}