{"id":"https://openalex.org/W4283520490","doi":"https://doi.org/10.1007/s40314-022-01926-y","title":"Nonlocal symmetry, exact solutions and conservation laws of the (1+1)-dimensional Levi equation","display_name":"Nonlocal symmetry, exact solutions and conservation laws of the (1+1)-dimensional Levi equation","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4283520490","doi":"https://doi.org/10.1007/s40314-022-01926-y"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-022-01926-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-022-01926-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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/A5049536967","display_name":"Yuru Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I196934937","display_name":"Liaocheng University","ror":"https://ror.org/03yh0n709","country_code":"CN","type":"education","lineage":["https://openalex.org/I196934937"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yuru Hu","raw_affiliation_strings":["School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-7289-8871","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People\u2019s Republic of China","institution_ids":["https://openalex.org/I196934937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100401234","display_name":"Feng Zhang","orcid":"https://orcid.org/0000-0002-1163-2498"},"institutions":[{"id":"https://openalex.org/I196934937","display_name":"Liaocheng University","ror":"https://ror.org/03yh0n709","country_code":"CN","type":"education","lineage":["https://openalex.org/I196934937"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Feng Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People\u2019s Republic of China","institution_ids":["https://openalex.org/I196934937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058526990","display_name":"Xiangpeng Xin","orcid":"https://orcid.org/0000-0003-2635-8265"},"institutions":[{"id":"https://openalex.org/I196934937","display_name":"Liaocheng University","ror":"https://ror.org/03yh0n709","country_code":"CN","type":"education","lineage":["https://openalex.org/I196934937"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangpeng Xin","raw_affiliation_strings":["School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Liaocheng University, Liaocheng, 252059, People\u2019s Republic of China","institution_ids":["https://openalex.org/I196934937"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049536967"],"corresponding_institution_ids":["https://openalex.org/I196934937"],"apc_list":null,"apc_paid":null,"fwci":0.3755,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.56259341,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"41","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":1.0,"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":1.0,"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":0.9965999722480774,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/riccati-equation","display_name":"Riccati equation","score":0.8992294073104858},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.7595697045326233},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.7308104038238525},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.6571880578994751},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6014963984489441},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.49188971519470215},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.45744889974594116},{"id":"https://openalex.org/keywords/soliton","display_name":"Soliton","score":0.45015236735343933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4207736849784851},{"id":"https://openalex.org/keywords/exact-differential-equation","display_name":"Exact differential equation","score":0.41036418080329895},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.406684547662735},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.3502551317214966},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3084833025932312},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2361443042755127},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.20364254713058472},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11951860785484314},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10468548536300659}],"concepts":[{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.8992294073104858},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.7595697045326233},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7308104038238525},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.6571880578994751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6014963984489441},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.49188971519470215},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.45744889974594116},{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.45015236735343933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4207736849784851},{"id":"https://openalex.org/C185184677","wikidata":"https://www.wikidata.org/wiki/Q1366795","display_name":"Exact differential equation","level":4,"score":0.41036418080329895},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.406684547662735},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.3502551317214966},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3084833025932312},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2361443042755127},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.20364254713058472},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11951860785484314},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10468548536300659},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-022-01926-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-022-01926-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G7743931902","display_name":null,"funder_award_id":"11505090","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1487989979","https://openalex.org/W1815469519","https://openalex.org/W1975249311","https://openalex.org/W2043465319","https://openalex.org/W2047624282","https://openalex.org/W2065007500","https://openalex.org/W2437761065","https://openalex.org/W2517335494","https://openalex.org/W2590414387","https://openalex.org/W2601546224","https://openalex.org/W2612660319","https://openalex.org/W2889334632","https://openalex.org/W2911249005","https://openalex.org/W3024417761","https://openalex.org/W3039020441","https://openalex.org/W3051203407","https://openalex.org/W3061625911","https://openalex.org/W3107497183","https://openalex.org/W3108555702","https://openalex.org/W3121701557","https://openalex.org/W3136589883","https://openalex.org/W3147190764","https://openalex.org/W3147527329","https://openalex.org/W3152777496","https://openalex.org/W3161170648","https://openalex.org/W3168190064","https://openalex.org/W3168314120","https://openalex.org/W3175409214","https://openalex.org/W3194620579","https://openalex.org/W3196654813","https://openalex.org/W3198927227","https://openalex.org/W4200551085","https://openalex.org/W4211044563","https://openalex.org/W4226034867"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2105459831","https://openalex.org/W1546579375","https://openalex.org/W2127238600","https://openalex.org/W1563296412","https://openalex.org/W2114791549","https://openalex.org/W16457797","https://openalex.org/W3023620176","https://openalex.org/W2111408487","https://openalex.org/W2040364519"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}