{"id":"https://openalex.org/W4390806724","doi":"https://doi.org/10.1137/23m155414x","title":"Optimal Error Bounds on the Exponential Wave Integrator for the Nonlinear Schr\u00f6dinger Equation with Low Regularity Potential and Nonlinearity","display_name":"Optimal Error Bounds on the Exponential Wave Integrator for the Nonlinear Schr\u00f6dinger Equation with Low Regularity Potential and Nonlinearity","publication_year":2024,"publication_date":"2024-01-11","ids":{"openalex":"https://openalex.org/W4390806724","doi":"https://doi.org/10.1137/23m155414x"},"language":"en","primary_location":{"id":"doi:10.1137/23m155414x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m155414x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"SIAM Journal on Numerical Analysis","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/A5100759028","display_name":"Weizhu Bao","orcid":"https://orcid.org/0000-0003-3418-9625"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Weizhu Bao","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, 119076 Singapore"],"raw_orcid":"https://orcid.org/0000-0003-3418-9625","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, 119076 Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013558597","display_name":"Chushan Wang","orcid":"https://orcid.org/0000-0002-7842-2495"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Chushan Wang","raw_affiliation_strings":["Department of Mathematics, National University of Singapore, 119076 Singapore"],"raw_orcid":"https://orcid.org/0000-0002-7842-2495","affiliations":[{"raw_affiliation_string":"Department of Mathematics, National University of Singapore, 119076 Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100759028"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":6.3516,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.97060059,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"62","issue":"1","first_page":"93","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9980000257492065,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9932000041007996,"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/mathematics","display_name":"Mathematics","score":0.7877360582351685},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6923121213912964},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.6350463032722473},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6221022605895996},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.599966824054718},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5688778162002563},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5559974908828735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5081868171691895},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.49115845561027527},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.4752925634384155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45843419432640076},{"id":"https://openalex.org/keywords/gauss-pseudospectral-method","display_name":"Gauss pseudospectral method","score":0.4111928343772888},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.3630157709121704},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.2410047948360443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12735989689826965},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10293892025947571}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7877360582351685},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6923121213912964},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.6350463032722473},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6221022605895996},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.599966824054718},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5688778162002563},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5559974908828735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5081868171691895},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.49115845561027527},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.4752925634384155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45843419432640076},{"id":"https://openalex.org/C71026131","wikidata":"https://www.wikidata.org/wiki/Q5527825","display_name":"Gauss pseudospectral method","level":5,"score":0.4111928343772888},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.3630157709121704},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2410047948360443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12735989689826965},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10293892025947571},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m155414x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m155414x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8559541805","display_name":null,"funder_award_id":"MOE-T2EP20122-0002 (A-8000962-00-00)","funder_id":"https://openalex.org/F4320320751","funder_display_name":"Ministry of Education - Singapore"}],"funders":[{"id":"https://openalex.org/F4320320751","display_name":"Ministry of Education - Singapore","ror":"https://ror.org/01kcva023"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W636566490","https://openalex.org/W2006043132","https://openalex.org/W2008869195","https://openalex.org/W2012220122","https://openalex.org/W2023195358","https://openalex.org/W2031375452","https://openalex.org/W2036516029","https://openalex.org/W2047594626","https://openalex.org/W2050338742","https://openalex.org/W2058992888","https://openalex.org/W2060005168","https://openalex.org/W2064278559","https://openalex.org/W2065476128","https://openalex.org/W2066944044","https://openalex.org/W2073821851","https://openalex.org/W2074531708","https://openalex.org/W2075696551","https://openalex.org/W2078210968","https://openalex.org/W2083561837","https://openalex.org/W2092400970","https://openalex.org/W2094788584","https://openalex.org/W2117988589","https://openalex.org/W2121676554","https://openalex.org/W2130655033","https://openalex.org/W2143619815","https://openalex.org/W2154993133","https://openalex.org/W2182274314","https://openalex.org/W2211454332","https://openalex.org/W2387639988","https://openalex.org/W2401777002","https://openalex.org/W2486911800","https://openalex.org/W2618966431","https://openalex.org/W2746957752","https://openalex.org/W2794394857","https://openalex.org/W2795033786","https://openalex.org/W2902944228","https://openalex.org/W2962865398","https://openalex.org/W2963738884","https://openalex.org/W2968362487","https://openalex.org/W3023795180","https://openalex.org/W3039811077","https://openalex.org/W3101047577","https://openalex.org/W3101835573","https://openalex.org/W3124588459","https://openalex.org/W3174006813","https://openalex.org/W3174693435","https://openalex.org/W3191571649","https://openalex.org/W3196426303","https://openalex.org/W3207433063","https://openalex.org/W3210061315","https://openalex.org/W4211077197","https://openalex.org/W4253937035","https://openalex.org/W4286971439","https://openalex.org/W4288459455","https://openalex.org/W4310663747","https://openalex.org/W4376959349","https://openalex.org/W4386476405"],"related_works":["https://openalex.org/W2357738898","https://openalex.org/W2356744059","https://openalex.org/W1512809069","https://openalex.org/W2761671048","https://openalex.org/W2550657075","https://openalex.org/W2143234151","https://openalex.org/W4388184483","https://openalex.org/W2359296948","https://openalex.org/W1974501530","https://openalex.org/W2085531723"],"abstract_inverted_index":{".We":[0],"establish":[1],"optimal":[2,48,92,140],"error":[3,169,190,214,231],"bounds":[4,191],"for":[5,119,197],"the":[6,13,27,33,36,41,62,73,77,83,114,129,132,146,153,167,172,183,194,198],"exponential":[7],"wave":[8,225],"integrator":[9],"(EWI)":[10],"applied":[11],"to":[12,182,211,217],"nonlinear":[14],"Schr\u00f6dinger":[15,223],"equation":[16],"(NLSE)":[17],"with":[18,56,67,200],"\\(":[19,30,49,53,57,70,93,97,110,120,135,141],"L^{\\infty":[20],"}\\)-potential":[21],"and/or":[22,204],"locally":[23],"Lipschitz":[24],"nonlinearity":[25,154],"under":[26,131],"assumption":[28,133],"of":[29,32,72,128,134,149],"H^2\\)-solution":[31],"NLSE.":[34],"For":[35,76],"semidiscretization":[37],"in":[38,87],"time":[39,63],"by":[40,81],"first-order":[42],"Gautschi-type":[43],"EWI,":[44],"we":[45,89,137,158],"prove":[46,90],"an":[47,91,139,160],"L^2\\)-error":[50,94],"bound":[51,95,170],"at":[52,96],"O(\\tau":[54,98],")\\)":[55],"\\tau":[58],"\\gt":[59],"0\\)":[60,112],"being":[61],"step":[64],"size,":[65],"together":[66],"a":[68,124],"uniform":[69],"H^2\\)-bound":[71],"numerical":[74,207],"solution.":[75],"full-discretization":[78],"scheme":[79],"obtained":[80],"using":[82],"Fourier":[84,162,173,185,233],"spectral":[85,174],"method":[86,164],"space,":[88],"+":[99],"h^2)\\)":[100],"without":[101],"any":[102],"coupling":[103],"condition":[104],"between":[105],"\\(\\tau\\)":[106],"and":[107,123,216],"\\(h\\),":[108],"where":[109],"h\\gt":[111],"is":[113,148,155,180],"mesh":[115],"size.":[116],"In":[117],"addition,":[118],"W^{1,":[121],"4}\\)-potential":[122],"little":[125],"stronger":[126],"regularity":[127,151,202,227,229],"nonlinearity,":[130],"H^3\\)-solution,":[136],"obtain":[138],"H^1\\)-error":[142],"bound.":[143],"Furthermore,":[144],"when":[145],"potential":[147,203],"low":[150,201],"but":[152],"sufficiently":[156],"smooth,":[157],"propose":[159],"extended":[161],"pseudospectral":[163,186,234],"which":[165],"has":[166],"same":[168],"as":[171],"method,":[175],"while":[176],"its":[177],"computational":[178],"cost":[179],"similar":[181],"standard":[184],"method.":[187],"Our":[188],"new":[189],"greatly":[192],"improve":[193],"existing":[195],"results":[196,208],"NLSE":[199],"nonlinearity.":[205],"Extensive":[206],"are":[209,221],"reported":[210],"confirm":[212],"our":[213],"estimates":[215],"demonstrate":[218],"that":[219],"they":[220],"sharp.Keywordsnonlinear":[222],"equationexponential":[224],"integratorlow":[226],"potentiallow":[228],"nonlinearityoptimal":[230],"boundextended":[232],"methodMSC":[235],"codes35Q5565M1565M7081Q05":[236]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}