{"id":"https://openalex.org/W1173936540","doi":"https://doi.org/10.1007/s00332-015-9272-7","title":"Liouville Correspondence Between the Modified KdV Hierarchy and Its Dual Integrable Hierarchy","display_name":"Liouville Correspondence Between the Modified KdV Hierarchy and Its Dual Integrable Hierarchy","publication_year":2015,"publication_date":"2015-08-25","ids":{"openalex":"https://openalex.org/W1173936540","doi":"https://doi.org/10.1007/s00332-015-9272-7","mag":"1173936540"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-015-9272-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-015-9272-7","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1404.5841","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103983806","display_name":"Jing Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I36819085","display_name":"Northwest University","ror":"https://ror.org/00y7snj24","country_code":"US","type":"education","lineage":["https://openalex.org/I36819085"]},{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Jing Kang","raw_affiliation_strings":["Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi\u2019an, 710069, People\u2019s Republic of China","NorthWest University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi\u2019an, 710069, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37802460"]},{"raw_affiliation_string":"NorthWest University","institution_ids":["https://openalex.org/I36819085"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100698267","display_name":"Xiaochuan Liu","orcid":"https://orcid.org/0000-0001-7575-8279"},"institutions":[{"id":"https://openalex.org/I36819085","display_name":"Northwest University","ror":"https://ror.org/00y7snj24","country_code":"US","type":"education","lineage":["https://openalex.org/I36819085"]},{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Xiaochuan Liu","raw_affiliation_strings":["Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi\u2019an, 710069, People\u2019s Republic of China","NorthWest University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi\u2019an, 710069, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37802460"]},{"raw_affiliation_string":"NorthWest University","institution_ids":["https://openalex.org/I36819085"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070840504","display_name":"Peter J. Olver","orcid":"https://orcid.org/0000-0001-6209-8777"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Peter J. Olver","raw_affiliation_strings":["School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA","University of\u00a0Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"University of\u00a0Minnesota","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102752385","display_name":"Changzheng Qu","orcid":"https://orcid.org/0000-0003-4859-367X"},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Changzheng Qu","raw_affiliation_strings":["Department of Mathematics, Ningbo University, Ningbo, 315211, People\u2019s Republic of China","Ningbo university"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ningbo University, Ningbo, 315211, People\u2019s Republic of China","institution_ids":["https://openalex.org/I109935558"]},{"raw_affiliation_string":"Ningbo university","institution_ids":["https://openalex.org/I109935558"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5070840504"],"corresponding_institution_ids":["https://openalex.org/I130238516"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.5516,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.88715089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"141","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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":0.9998999834060669,"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9736999869346619,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9708999991416931,"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-system","display_name":"Integrable system","score":0.921536922454834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7713022232055664},{"id":"https://openalex.org/keywords/camassa\u2013holm-equation","display_name":"Camassa\u2013Holm equation","score":0.7605910301208496},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.701982855796814},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6828627586364746},{"id":"https://openalex.org/keywords/isospectral","display_name":"Isospectral","score":0.6824003458023071},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.6714823246002197},{"id":"https://openalex.org/keywords/lax-pair","display_name":"Lax pair","score":0.5915638208389282},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5696382522583008},{"id":"https://openalex.org/keywords/kdv-hierarchy","display_name":"KdV hierarchy","score":0.5499703884124756},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4953228533267975},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.47998806834220886},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.47296255826950073},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4200586676597595},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4192821979522705},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37408772110939026},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1257132589817047},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.08921799063682556},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07661610841751099},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.06406092643737793}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.921536922454834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7713022232055664},{"id":"https://openalex.org/C24454023","wikidata":"https://www.wikidata.org/wiki/Q5025006","display_name":"Camassa\u2013Holm equation","level":3,"score":0.7605910301208496},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.701982855796814},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6828627586364746},{"id":"https://openalex.org/C2779710842","wikidata":"https://www.wikidata.org/wiki/Q6086323","display_name":"Isospectral","level":2,"score":0.6824003458023071},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.6714823246002197},{"id":"https://openalex.org/C172829509","wikidata":"https://www.wikidata.org/wiki/Q4115796","display_name":"Lax pair","level":3,"score":0.5915638208389282},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5696382522583008},{"id":"https://openalex.org/C2779148545","wikidata":"https://www.wikidata.org/wiki/Q6382014","display_name":"KdV hierarchy","level":4,"score":0.5499703884124756},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4953228533267975},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.47998806834220886},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.47296255826950073},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4200586676597595},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4192821979522705},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37408772110939026},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1257132589817047},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.08921799063682556},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07661610841751099},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.06406092643737793},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00332-015-9272-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00332-015-9272-7","pdf_url":null,"source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"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":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1404.5841","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.5841","pdf_url":"https://arxiv.org/pdf/1404.5841","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1404.5841","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.5841","pdf_url":"https://arxiv.org/pdf/1404.5841","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15","score":0.6800000071525574}],"awards":[{"id":"https://openalex.org/G2947296526","display_name":null,"funder_award_id":"DMS-1108894","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"}],"funders":[{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1173936540.pdf","grobid_xml":"https://content.openalex.org/works/W1173936540.grobid-xml"},"referenced_works_count":110,"referenced_works":["https://openalex.org/W80359875","https://openalex.org/W99189181","https://openalex.org/W316919195","https://openalex.org/W579093851","https://openalex.org/W1492711015","https://openalex.org/W1494563177","https://openalex.org/W1510817630","https://openalex.org/W1542177822","https://openalex.org/W1551335708","https://openalex.org/W1573927207","https://openalex.org/W1887903210","https://openalex.org/W1893670732","https://openalex.org/W1919113267","https://openalex.org/W1967771793","https://openalex.org/W1967881588","https://openalex.org/W1968435495","https://openalex.org/W1968778597","https://openalex.org/W1978505290","https://openalex.org/W1979855427","https://openalex.org/W1982693832","https://openalex.org/W1983920324","https://openalex.org/W1987233115","https://openalex.org/W1988878611","https://openalex.org/W1988934258","https://openalex.org/W1989102406","https://openalex.org/W1993068124","https://openalex.org/W1994309388","https://openalex.org/W1997301295","https://openalex.org/W1999170261","https://openalex.org/W2004725010","https://openalex.org/W2009433941","https://openalex.org/W2015363211","https://openalex.org/W2016767879","https://openalex.org/W2022710727","https://openalex.org/W2024526947","https://openalex.org/W2026031976","https://openalex.org/W2028569106","https://openalex.org/W2032084627","https://openalex.org/W2033270072","https://openalex.org/W2038631673","https://openalex.org/W2039190309","https://openalex.org/W2040539582","https://openalex.org/W2040821216","https://openalex.org/W2041234363","https://openalex.org/W2043191176","https://openalex.org/W2045425785","https://openalex.org/W2046078856","https://openalex.org/W2048017269","https://openalex.org/W2049395465","https://openalex.org/W2049412500","https://openalex.org/W2050111134","https://openalex.org/W2050255278","https://openalex.org/W2052528969","https://openalex.org/W2055562998","https://openalex.org/W2057545369","https://openalex.org/W2057817591","https://openalex.org/W2058319209","https://openalex.org/W2061191702","https://openalex.org/W2062572188","https://openalex.org/W2064108635","https://openalex.org/W2064355804","https://openalex.org/W2068146456","https://openalex.org/W2069149882","https://openalex.org/W2069460357","https://openalex.org/W2069891873","https://openalex.org/W2070352888","https://openalex.org/W2071969012","https://openalex.org/W2072210701","https://openalex.org/W2084217855","https://openalex.org/W2087124855","https://openalex.org/W2087137871","https://openalex.org/W2087235722","https://openalex.org/W2088668919","https://openalex.org/W2090814006","https://openalex.org/W2093785095","https://openalex.org/W2094057156","https://openalex.org/W2104916047","https://openalex.org/W2119443761","https://openalex.org/W2120574708","https://openalex.org/W2122794051","https://openalex.org/W2123974695","https://openalex.org/W2134878012","https://openalex.org/W2136437647","https://openalex.org/W2142285825","https://openalex.org/W2143631463","https://openalex.org/W2157901810","https://openalex.org/W2160308438","https://openalex.org/W2161164203","https://openalex.org/W2169938087","https://openalex.org/W2251214233","https://openalex.org/W2479395228","https://openalex.org/W2739434761","https://openalex.org/W2741455208","https://openalex.org/W3021535703","https://openalex.org/W3040940214","https://openalex.org/W3100288554","https://openalex.org/W3104045352","https://openalex.org/W3105128049","https://openalex.org/W3106514252","https://openalex.org/W3147477880","https://openalex.org/W4210329888","https://openalex.org/W4211202937","https://openalex.org/W4214685161","https://openalex.org/W4214790298","https://openalex.org/W4232982029","https://openalex.org/W4238691109","https://openalex.org/W4241682055","https://openalex.org/W4251375806","https://openalex.org/W4292170110","https://openalex.org/W4366309888"],"related_works":["https://openalex.org/W2329242664","https://openalex.org/W3144639764","https://openalex.org/W2093091422","https://openalex.org/W1480313473","https://openalex.org/W1995258415","https://openalex.org/W4213214954","https://openalex.org/W2787051621","https://openalex.org/W3093151310","https://openalex.org/W2004175720","https://openalex.org/W2371762260"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":2}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2016-06-24T00:00:00"}