{"id":"https://openalex.org/W2110976139","doi":"https://doi.org/10.1155/s0161171202106120","title":"The averaging of nonlocal Hamiltonian structures in Whitham\u2032s method","display_name":"The averaging of nonlocal Hamiltonian structures in Whitham\u2032s method","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2110976139","doi":"https://doi.org/10.1155/s0161171202106120","mag":"2110976139"},"language":"en","primary_location":{"id":"doi:10.1155/s0161171202106120","doi":"https://doi.org/10.1155/s0161171202106120","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171202106120","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2002/296321.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2002/296321.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003299406","display_name":"Andrei Ya Mal'tsev","orcid":"https://orcid.org/0000-0001-7634-1811","observed_orcids":["https://orcid.org/0000-0001-7634-1811"]},"institutions":[{"id":"https://openalex.org/I138549579","display_name":"Scuola Internazionale Superiore di Studi Avanzati","ror":"https://ror.org/004fze387","country_code":"IT","type":"education","lineage":["https://openalex.org/I138549579"]},{"id":"https://openalex.org/I196576671","display_name":"Landau Institute for Theoretical Physics","ror":"https://ror.org/00z65ng94","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I196576671","https://openalex.org/I4210096333"]}],"countries":["IT","RU"],"is_corresponding":true,"raw_author_name":"Andrei Ya. Maltsev","raw_affiliation_strings":["Landau Institute for Theoretical Physics, 117940, Kosygina 2, Moscow","SISSA-ISAS, Via Beirut 2-4, Trieste 34014"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Landau Institute for Theoretical Physics, 117940, Kosygina 2, Moscow","institution_ids":["https://openalex.org/I196576671"]},{"raw_affiliation_string":"SISSA-ISAS, Via Beirut 2-4, Trieste 34014","institution_ids":["https://openalex.org/I138549579"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003299406"],"corresponding_institution_ids":["https://openalex.org/I138549579","https://openalex.org/I196576671"],"apc_list":{"value":1240,"currency":"USD","value_usd":1240},"apc_paid":{"value":1240,"currency":"USD","value_usd":1240},"fwci":0.8359,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.75168539,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"30","issue":"7","first_page":"399","last_page":"434"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.00039999998989515007,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/integrable-systems","display_name":"integrable systems","score":0.6940000057220459}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7796875238418579},{"id":"https://openalex.org/C188845816","wikidata":"https://www.wikidata.org/wiki/Q1052775","display_name":"Poisson bracket","level":3,"score":0.7766005992889404},{"id":"https://openalex.org/C114170632","wikidata":"https://www.wikidata.org/wiki/Q2003641","display_name":"Novikov self-consistency principle","level":2,"score":0.6954636573791504},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6209118962287903},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5711135864257812},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5453904867172241},{"id":"https://openalex.org/C4161247","wikidata":"https://www.wikidata.org/wiki/Q11143305","display_name":"Poisson algebra","level":4,"score":0.45513665676116943},{"id":"https://openalex.org/C133769200","wikidata":"https://www.wikidata.org/wiki/Q174565","display_name":"Bracket","level":2,"score":0.4453147053718567},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4149370491504669},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3996937870979309},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3805793225765228},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34527474641799927},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13551875948905945},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.057075053453445435},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.054047584533691406},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/s0161171202106120","doi":"https://doi.org/10.1155/s0161171202106120","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171202106120","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2002/296321.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:48d4f12e81674c28a03901854fe348b5","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/48d4f12e81674c28a03901854fe348b5","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 30, Iss 7, Pp 399-434 (2002)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/s0161171202106120","doi":"https://doi.org/10.1155/s0161171202106120","is_oa":true,"landing_page_url":"https://doi.org/10.1155/s0161171202106120","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2002/296321.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4618969666","display_name":null,"funder_award_id":"97-01-00281","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2110976139.pdf","grobid_xml":"https://content.openalex.org/works/W2110976139.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W148085258","https://openalex.org/W305332711","https://openalex.org/W317867062","https://openalex.org/W623103843","https://openalex.org/W1520515963","https://openalex.org/W1969892217","https://openalex.org/W1973107894","https://openalex.org/W1981683093","https://openalex.org/W1984417688","https://openalex.org/W1986788497","https://openalex.org/W1990414802","https://openalex.org/W1998114903","https://openalex.org/W2008043408","https://openalex.org/W2035979363","https://openalex.org/W2044644513","https://openalex.org/W2048546986","https://openalex.org/W2049884677","https://openalex.org/W2056071888","https://openalex.org/W2060308659","https://openalex.org/W2071828573","https://openalex.org/W2072898679","https://openalex.org/W2080649760","https://openalex.org/W2090654842","https://openalex.org/W2095723741","https://openalex.org/W2155804277","https://openalex.org/W2329297216","https://openalex.org/W2963679990","https://openalex.org/W4229830887","https://openalex.org/W6600122344","https://openalex.org/W6600765635","https://openalex.org/W6606074631","https://openalex.org/W6608364376","https://openalex.org/W6639605363","https://openalex.org/W6738286617","https://openalex.org/W6796789798","https://openalex.org/W6832611370"],"related_works":["https://openalex.org/W2963699997","https://openalex.org/W2113537957","https://openalex.org/W1627747318","https://openalex.org/W1972173854","https://openalex.org/W2077200343","https://openalex.org/W3212018","https://openalex.org/W2001618980","https://openalex.org/W2012663946","https://openalex.org/W2030028867","https://openalex.org/W1965531411"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,9,21,31,35,50,53,57],"m\u2010phase":[3],"Whitham\u2032s":[4,42],"averaging":[5],"method":[6,45],"and":[7,33],"propose":[8],"procedure":[10,17,55],"of":[11,23,27,30,38,52],"\u201caveraging\u201d":[12],"nonlocal":[13],"Hamiltonian":[14],"structures.":[15],"The":[16,44],"is":[18],"based":[19],"on":[20],"existence":[22],"a":[24],"sufficient":[25],"number":[26],"local\u2010commuting":[28],"integrals":[29],"system":[32],"gives":[34],"Poisson":[36],"bracket":[37],"Ferapontov":[39],"type":[40],"for":[41,56],"system.":[43],"can":[46],"be":[47],"considered":[48],"as":[49],"generalization":[51],"Dubrovin\u2010Novikov":[54],"local":[58],"field\u2010theoretical":[59],"brackets.":[60]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}