{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:40:20Z","timestamp":1761676820960,"version":"3.41.2"},"reference-count":20,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T00:00:00Z","timestamp":1572307200000},"content-version":"vor","delay-in-days":301,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11775104"],"award-info":[{"award-number":["11775104"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The residual symmetry of a negative\u2010order Korteweg\u2013de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the original nKdV equation is extended into an enlarged system by introducing four new variables. By using Lie\u2019s first theorem, we obtain the finite transformation for the localized residual symmetry. Furthermore, we localize the linear superposition of multiple residual symmetries and construct <jats:italic>n<\/jats:italic>\u2010th B\u00e4cklund transformation for this nKdV equation in the form of the determinants.<\/jats:p>","DOI":"10.1155\/2019\/5479695","type":"journal-article","created":{"date-parts":[[2019,10,29]],"date-time":"2019-10-29T23:30:47Z","timestamp":1572391847000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Nonlocal Symmetry and B\u00e4cklund Transformation of a Negative\u2010Order Korteweg\u2013de Vries Equation"],"prefix":"10.1155","volume":"2019","author":[{"given":"Jinxi","family":"Fei","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9684-4835","authenticated-orcid":false,"given":"Weiping","family":"Cao","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5389-2052","authenticated-orcid":false,"given":"Zhengyi","family":"Ma","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,10,29]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1080\/14786449508620739"},{"key":"e_1_2_8_2_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.523393"},{"key":"e_1_2_8_3_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.529234"},{"key":"e_1_2_8_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2017.05.002"},{"key":"e_1_2_8_5_2","doi-asserted-by":"publisher","DOI":"10.1515\/zna-2017-0191"},{"key":"e_1_2_8_6_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.530509"},{"key":"e_1_2_8_7_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/94\/50003"},{"key":"e_1_2_8_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(96)00048-6"},{"key":"e_1_2_8_9_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.3257918"},{"key":"e_1_2_8_10_2","doi-asserted-by":"publisher","DOI":"10.1002\/mma.3507"},{"key":"e_1_2_8_11_2","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.79.063835"},{"key":"e_1_2_8_12_2","doi-asserted-by":"publisher","DOI":"10.1080\/17455030.2017.1367440"},{"key":"e_1_2_8_13_2","doi-asserted-by":"publisher","DOI":"10.1088\/0031-8949\/57\/4\/001"},{"key":"e_1_2_8_14_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.86.016601"},{"key":"e_1_2_8_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(96)00095-3"},{"key":"e_1_2_8_16_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.1532769"},{"volume-title":"Finite-dimensional Integrable System and Nonlinear Evolution Equations","year":"2002","author":"Qiao Z. J.","key":"e_1_2_8_17_2"},{"key":"e_1_2_8_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40010-017-0349-6"},{"key":"e_1_2_8_19_2","unstructured":"KudryashovN. A. On completely integrability systems of differential equations 2010 http:\/\/arxiv.org\/abs\/1011.3936v1."},{"key":"e_1_2_8_20_2","unstructured":"KudryashovN. A. Unnecessary exact solutions of nonlinear ordinary differential equations 2010 http:\/\/arxiv.org\/abs\/1011.1623v1."}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/5479695.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2019\/5479695.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2019\/5479695","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T11:33:45Z","timestamp":1723030425000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2019\/5479695"}},"subtitle":[],"editor":[{"given":"Robert","family":"Hakl","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":20,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1155\/2019\/5479695"],"URL":"https:\/\/doi.org\/10.1155\/2019\/5479695","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2019,1]]},"assertion":[{"value":"2019-07-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-09-17","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-10-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5479695"}}