{"id":"https://openalex.org/W2095377487","doi":"https://doi.org/10.1137/110831222","title":"Numerical Computation of Solutions of the Critical Nonlinear Schr\u00f6dinger Equation after the Singularity","display_name":"Numerical Computation of Solutions of the Critical Nonlinear Schr\u00f6dinger Equation after the Singularity","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2095377487","doi":"https://doi.org/10.1137/110831222","mag":"2095377487"},"language":"en","primary_location":{"id":"doi:10.1137/110831222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110831222","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","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/A5078411693","display_name":"Panos Stinis","orcid":"https://orcid.org/0000-0002-9928-5637"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Panos Stinis","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5078411693"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2302,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76738822,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"1","first_page":"48","last_page":"60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9983000159263611,"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/singularity","display_name":"Singularity","score":0.9220828413963318},{"id":"https://openalex.org/keywords/formalism","display_name":"Formalism (music)","score":0.748805820941925},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6460682153701782},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6026232838630676},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5301170349121094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5251138806343079},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4813012182712555},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.468863308429718},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44583746790885925},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.4169454872608185},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.39579057693481445},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.33998534083366394},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3139533996582031},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07657599449157715},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.04963350296020508}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.9220828413963318},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.748805820941925},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6460682153701782},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6026232838630676},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5301170349121094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5251138806343079},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4813012182712555},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.468863308429718},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44583746790885925},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.4169454872608185},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.39579057693481445},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33998534083366394},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3139533996582031},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07657599449157715},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.04963350296020508},{"id":"https://openalex.org/C558565934","wikidata":"https://www.wikidata.org/wiki/Q2743","display_name":"Musical","level":2,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110831222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110831222","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","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":18,"referenced_works":["https://openalex.org/W189499540","https://openalex.org/W1547431580","https://openalex.org/W1601100443","https://openalex.org/W1995634600","https://openalex.org/W2028119371","https://openalex.org/W2030328882","https://openalex.org/W2080865216","https://openalex.org/W2088626733","https://openalex.org/W2101116262","https://openalex.org/W2105061081","https://openalex.org/W2105940671","https://openalex.org/W2117980206","https://openalex.org/W2156603435","https://openalex.org/W2164193727","https://openalex.org/W2596697493","https://openalex.org/W2963115651","https://openalex.org/W2963559789","https://openalex.org/W3209416867"],"related_works":["https://openalex.org/W2351083540","https://openalex.org/W2039808196","https://openalex.org/W2245214771","https://openalex.org/W2333053900","https://openalex.org/W1975562467","https://openalex.org/W2951961089","https://openalex.org/W3101208931","https://openalex.org/W2181923191","https://openalex.org/W3213209941","https://openalex.org/W2074095400"],"abstract_inverted_index":{"We":[0,28],"present":[1],"numerical":[2],"results":[3],"for":[4],"the":[5,8,31,42,45,48,55,59],"solution":[6,43,53],"of":[7,47],"one-dimensional":[9],"critical":[10],"nonlinear":[11],"Schr\u00f6dinger":[12],"with":[13],"periodic":[14],"boundary":[15],"conditions":[16],"and":[17],"initial":[18],"data":[19],"that":[20],"give":[21],"rise":[22],"to":[23,40],"a":[24,34],"finite":[25],"time":[26],"singularity.":[27,49],"construct,":[29],"through":[30],"Mori\u2013Zwanzig":[32],"formalism,":[33],"reduced":[35],"model":[36],"which":[37],"allows":[38],"us":[39],"follow":[41],"after":[44],"formation":[46],"The":[50],"computed":[51],"postsingularity":[52,60],"exhibits":[54],"same":[56],"characteristics":[57],"as":[58],"solutions":[61],"constructed":[62],"recently":[63],"by":[64],"Terence":[65],"Tao.":[66]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
