{"id":"https://openalex.org/W2063455080","doi":"https://doi.org/10.1155/2012/346824","title":"A Class of PDEs with Nonlinear Superposition Principles","display_name":"A Class of PDEs with Nonlinear Superposition Principles","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2063455080","doi":"https://doi.org/10.1155/2012/346824","mag":"2063455080"},"language":"en","primary_location":{"id":"doi:10.1155/2012/346824","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/346824","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/346824.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2012/346824.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100432721","display_name":"Peng Li","orcid":"https://orcid.org/0000-0002-5876-2177"},"institutions":[{"id":"https://openalex.org/I198645480","display_name":"North China University of Water Resources and Electric Power","ror":"https://ror.org/03acrzv41","country_code":"CN","type":"education","lineage":["https://openalex.org/I198645480"]},{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Peng","raw_affiliation_strings":["Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, China","School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061, China","Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011","School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, China","institution_ids":["https://openalex.org/I198645480"]},{"raw_affiliation_string":"School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011","institution_ids":["https://openalex.org/I198645480"]},{"raw_affiliation_string":"School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061","institution_ids":["https://openalex.org/I87445476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101475796","display_name":"Keying Liu","orcid":"https://orcid.org/0000-0002-6453-9908"},"institutions":[{"id":"https://openalex.org/I198645480","display_name":"North China University of Water Resources and Electric Power","ror":"https://ror.org/03acrzv41","country_code":"CN","type":"education","lineage":["https://openalex.org/I198645480"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu Keying","raw_affiliation_strings":["Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, China","Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, China","institution_ids":["https://openalex.org/I198645480"]},{"raw_affiliation_string":"Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011","institution_ids":["https://openalex.org/I198645480"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109193482","display_name":"Zuliang Pan","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pan Zuliang","raw_affiliation_strings":["Department of Mathematics, Zhejiang University, Hangzhou 310027, China","Department of Mathematics, Zhejiang University, Hangzhou 310027"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Zhejiang University, Hangzhou 310027, China","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"Department of Mathematics, Zhejiang University, Hangzhou 310027","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101547864","display_name":"Weizhou Zhong","orcid":"https://orcid.org/0000-0003-0966-2599"},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhong Weizhou","raw_affiliation_strings":["School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061, China","School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061"],"affiliations":[{"raw_affiliation_string":"School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061, China","institution_ids":["https://openalex.org/I87445476"]},{"raw_affiliation_string":"School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101547864"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.12100744,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"2012","issue":"1","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":0.9975000023841858,"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":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/superposition-principle","display_name":"Superposition principle","score":0.7287605404853821},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.7208091020584106},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.7154061198234558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7119717597961426},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6965129971504211},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6483789682388306},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6429585218429565},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.5004754066467285},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4969632923603058},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4968240559101105},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.4869164228439331},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4750012159347534},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3484794795513153},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.18324324488639832},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12845873832702637},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07852223515510559}],"concepts":[{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.7287605404853821},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.7208091020584106},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.7154061198234558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7119717597961426},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6965129971504211},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6483789682388306},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6429585218429565},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5004754066467285},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4969632923603058},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4968240559101105},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4869164228439331},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4750012159347534},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3484794795513153},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.18324324488639832},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12845873832702637},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07852223515510559},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2012/346824","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/346824","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/346824.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1355495099","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jam/1355495099","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:346824","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2012/346824.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:6340c16a95824169a68282c82d8df724","is_oa":true,"landing_page_url":"https://doaj.org/article/6340c16a95824169a68282c82d8df724","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2012 (2012)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2012/346824","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2012/346824","pdf_url":"https://downloads.hindawi.com/journals/jam/2012/346824.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2063455080.pdf","grobid_xml":"https://content.openalex.org/works/W2063455080.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1573927207","https://openalex.org/W1997632432","https://openalex.org/W2018364583","https://openalex.org/W2025559654","https://openalex.org/W2043317129","https://openalex.org/W2045384647","https://openalex.org/W2047774430","https://openalex.org/W2085296100","https://openalex.org/W2092647568","https://openalex.org/W2094106529","https://openalex.org/W2111881148","https://openalex.org/W2319678355","https://openalex.org/W2565432921","https://openalex.org/W2597461921","https://openalex.org/W2797256054","https://openalex.org/W4205708594","https://openalex.org/W4229672964"],"related_works":["https://openalex.org/W4308749380","https://openalex.org/W2044787408","https://openalex.org/W4249228129","https://openalex.org/W3104927070","https://openalex.org/W2040820615","https://openalex.org/W2086585817","https://openalex.org/W155593081","https://openalex.org/W2738038633","https://openalex.org/W1506619710","https://openalex.org/W2052607948"],"abstract_inverted_index":{"Through":[0],"assuming":[1],"that":[2,25,62],"nonlinear":[3,38],"superposition":[4],"principles":[5],"(NLSPs)":[6],"are":[7,40,58],"embedded":[8],"in":[9],"a":[10,13,21],"Lie":[11],"group,":[12],"class":[14],"of":[15,55,71],"3rd\u2010order":[16],"PDEs":[17,57],"is":[18,46],"derived":[19],"from":[20],"general":[22],"determining":[23],"equation":[24],"determine":[26],"the":[27,37,43,51,56,63],"invariant":[28],"group.":[29],"The":[30],"corresponding":[31],"NLSPs":[32],"and":[33],"transformation":[34],"to":[35],"linearize":[36],"PDE":[39,45],"found,":[41],"hence":[42],"governing":[44],"proved":[47],"C":[48],"\u2010integrable.":[49],"In":[50],"end,":[52],"some":[53],"applications":[54],"explained,":[59],"which":[60],"shows":[61],"result":[64],"has":[65],"very":[66],"subtle":[67],"relations":[68],"with":[69],"linearization":[70],"partial":[72],"differential":[73],"equation.":[74]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
