{"id":"https://openalex.org/W1988469123","doi":"https://doi.org/10.1007/s10208-010-9063-3","title":"Splitting Integrators for Nonlinear Schr\u00f6dinger Equations Over Long Times","display_name":"Splitting Integrators for Nonlinear Schr\u00f6dinger Equations Over Long Times","publication_year":2010,"publication_date":"2010-02-24","ids":{"openalex":"https://openalex.org/W1988469123","doi":"https://doi.org/10.1007/s10208-010-9063-3","mag":"1988469123"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-010-9063-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-010-9063-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","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/A5082832432","display_name":"Ludwig J. Gauckler","orcid":"https://orcid.org/0000-0002-7066-1715"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Ludwig Gauckler","raw_affiliation_strings":["Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, D-72076, T\u00fcbingen, Germany","Universit\u00e4t T\u00fcbingen, Mathematisches Institut, Auf der Morgenstelle 10, D-72076 T\u00fcbingen, Germany;"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, D-72076, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]},{"raw_affiliation_string":"Universit\u00e4t T\u00fcbingen, Mathematisches Institut, Auf der Morgenstelle 10, D-72076 T\u00fcbingen, Germany;","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":["Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, D-72076, T\u00fcbingen, Germany","Universit\u00e4t T\u00fcbingen, Mathematisches Institut, Auf der Morgenstelle 10, D-72076 T\u00fcbingen, Germany;"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle 10, D-72076, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]},{"raw_affiliation_string":"Universit\u00e4t T\u00fcbingen, Mathematisches Institut, Auf der Morgenstelle 10, D-72076 T\u00fcbingen, Germany;","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5082832432"],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.598,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.90420891,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"10","issue":"3","first_page":"275","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9994999766349792,"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":0.9984999895095825,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.996399998664856,"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/discretization","display_name":"Discretization","score":0.8632696866989136},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8499249219894409},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6257123947143555},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5965991020202637},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.5681759715080261},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5676637291908264},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5581978559494019},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5497905015945435},{"id":"https://openalex.org/keywords/nonlinear-schr\u00f6dinger-equation","display_name":"Nonlinear Schr\u00f6dinger equation","score":0.5483785271644592},{"id":"https://openalex.org/keywords/split-step-method","display_name":"Split-step method","score":0.5267699956893921},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4341178238391876},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4306437075138092},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42774498462677},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.41826942563056946},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35825616121292114},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14912432432174683},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08567717671394348},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07542893290519714}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8632696866989136},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8499249219894409},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6257123947143555},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5965991020202637},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.5681759715080261},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5676637291908264},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5581978559494019},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5497905015945435},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.5483785271644592},{"id":"https://openalex.org/C134206417","wikidata":"https://www.wikidata.org/wiki/Q2311789","display_name":"Split-step method","level":3,"score":0.5267699956893921},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4341178238391876},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4306437075138092},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42774498462677},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.41826942563056946},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35825616121292114},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14912432432174683},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08567717671394348},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07542893290519714},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"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:10.1007/s10208-010-9063-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-010-9063-3","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.7099999785423279}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1544770838","https://openalex.org/W1718553958","https://openalex.org/W1719852618","https://openalex.org/W1963632370","https://openalex.org/W1967673736","https://openalex.org/W1970979424","https://openalex.org/W1972140872","https://openalex.org/W1995586597","https://openalex.org/W1996164347","https://openalex.org/W1997190030","https://openalex.org/W2026509625","https://openalex.org/W2031373684","https://openalex.org/W2093563917","https://openalex.org/W2144522531","https://openalex.org/W2947056241"],"related_works":["https://openalex.org/W2978232372","https://openalex.org/W2245214771","https://openalex.org/W1521863058","https://openalex.org/W2073973926","https://openalex.org/W4321141511","https://openalex.org/W4315645228","https://openalex.org/W2333053900","https://openalex.org/W2951961089","https://openalex.org/W3101208931","https://openalex.org/W1975562467"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}