{"id":"https://openalex.org/W1964582830","doi":"https://doi.org/10.1103/physrevlett.47.717","title":"Quantitive Theory of the Fermi-Pasta-Ulam Recurrence in the Nonlinear Schr\u00f6dinger Equation","display_name":"Quantitive Theory of the Fermi-Pasta-Ulam Recurrence in the Nonlinear Schr\u00f6dinger Equation","publication_year":1981,"publication_date":"1981-09-07","ids":{"openalex":"https://openalex.org/W1964582830","doi":"https://doi.org/10.1103/physrevlett.47.717","mag":"1964582830"},"language":"en","primary_location":{"id":"doi:10.1103/physrevlett.47.717","doi":"https://doi.org/10.1103/physrevlett.47.717","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevlett.47.717","pdf_url":null,"source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5072230979","display_name":"E. Infeld","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210097150","display_name":"National Centre for Nuclear Research","ror":"https://ror.org/00nzsxq20","country_code":"PL","type":"government","lineage":["https://openalex.org/I4210097150"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"E. Infeld","raw_affiliation_strings":["Institute of Nuclear Research, 00-681 Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Nuclear Research, 00-681 Warsaw, Poland","institution_ids":["https://openalex.org/I4210097150"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5072230979"],"corresponding_institution_ids":["https://openalex.org/I4210097150"],"apc_list":{"value":3750,"currency":"USD","value_usd":3750},"apc_paid":null,"fwci":0.313,"has_fulltext":false,"cited_by_count":94,"citation_normalized_percentile":{"value":0.4807806,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"47","issue":"10","first_page":"717","last_page":"718"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9473000168800354,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9473000168800354,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.042500000447034836,"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/T11603","display_name":"Dust and Plasma Wave Phenomena","score":0.0017000000225380063,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/fermi-pasta-ulam-recurrence","display_name":"Fermi-Pasta-Ulam recurrence","score":0.9940000176429749},{"id":"https://openalex.org/keywords/nonlinear-schrodinger-equation","display_name":"nonlinear Schr\u00f6dinger equation","score":0.9959999918937683},{"id":"https://openalex.org/keywords/time-to-recurrence","display_name":"time to recurrence","score":0.6499999761581421},{"id":"https://openalex.org/keywords/fourier-modes","display_name":"Fourier modes","score":0.8119999766349792},{"id":"https://openalex.org/keywords/plasma-physics","display_name":"plasma physics","score":0.7929999828338623},{"id":"https://openalex.org/keywords/gravity-waves","display_name":"gravity waves","score":0.7350000143051147},{"id":"https://openalex.org/keywords/deep-water-waves","display_name":"deep water waves","score":0.7480000257492065},{"id":"https://openalex.org/keywords/envelope-dynamics","display_name":"envelope dynamics","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.8059102296829224},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.6392582654953003},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6164705157279968},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6142835021018982},{"id":"https://openalex.org/C83774755","wikidata":"https://www.wikidata.org/wiki/Q2579914","display_name":"Nonlinear Schr\u00f6dinger equation","level":3,"score":0.5202173590660095},{"id":"https://openalex.org/C186769553","wikidata":"https://www.wikidata.org/wiki/Q726648","display_name":"Fermi Gamma-ray Space Telescope","level":2,"score":0.4809674322605133},{"id":"https://openalex.org/C3079626","wikidata":"https://www.wikidata.org/wiki/Q234881","display_name":"Quantum electrodynamics","level":1,"score":0.46817201375961304},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.46065589785575867},{"id":"https://openalex.org/C82706917","wikidata":"https://www.wikidata.org/wiki/Q10251","display_name":"Plasma","level":2,"score":0.4143299162387848},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3340100646018982},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3218306303024292},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1103/physrevlett.47.717","doi":"https://doi.org/10.1103/physrevlett.47.717","is_oa":false,"landing_page_url":"https://doi.org/10.1103/physrevlett.47.717","pdf_url":null,"source":{"id":"https://openalex.org/S24807848","display_name":"Physical Review Letters","issn_l":"0031-9007","issn":["0031-9007","1079-7114","1092-0145"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","ki-jl-2","medline","norway-2","poland-200","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320261","host_organization_name":"American Physical Society","host_organization_lineage":["https://openalex.org/P4310320261"],"host_organization_lineage_names":["American Physical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Physical Review Letters","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2055623556","https://openalex.org/W2058385818","https://openalex.org/W2059979131","https://openalex.org/W2081400025","https://openalex.org/W2100625455","https://openalex.org/W2131895465","https://openalex.org/W2328079520"],"related_works":["https://openalex.org/W2000903714","https://openalex.org/W2067498130","https://openalex.org/W7101073267","https://openalex.org/W2059979131","https://openalex.org/W2963956677","https://openalex.org/W2240334666","https://openalex.org/W2081417839","https://openalex.org/W3172555443","https://openalex.org/W1975511901","https://openalex.org/W2287647470"],"abstract_inverted_index":{"By":[0],"limiting":[1],"attention":[2],"to":[3],"the":[4,13,25,29,32,36,46,60,63,66,75],"lowest-order":[5],"Fourier":[6],"modes":[7],"we":[8],"obtain":[9],"a":[10,70],"theory":[11],"of":[12,28,35,45,62,65,69],"Fermi-Pasta-Ulam":[14],"recurrence":[15,30],"that":[16],"gives":[17],"excellent":[18],"agreement":[19],"with":[20],"recent":[21],"numerical":[22],"results.":[23],"Both":[24],"predicted":[26],"period":[27],"and":[31],"temporal":[33],"development":[34,61],"$n=0$":[37],"mode":[38],"are":[39],"very":[40],"good":[41],"fits.":[42],"The":[43],"maximum":[44],"$n=1$":[47],"mode,":[48],"however,":[49],"is":[50],"off":[51],"by":[52],"about":[53],"30%.":[54],"(The":[55],"nonlinear":[56,71],"Schr\\\"odinger":[57],"equation":[58],"governs":[59],"envelope":[64],"electric":[67],"field":[68],"Langmuir":[72],"wave":[73],"in":[74,83],"plasma-physics":[76],"context.":[77],"It":[78],"also":[79],"describes":[80],"gravity":[81],"waves":[82],"deep":[84],"water.)":[85]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
