{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T17:38:58Z","timestamp":1758476338350,"version":"3.41.2"},"reference-count":36,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2019,7,28]],"date-time":"2019-07-28T00:00:00Z","timestamp":1564272000000},"content-version":"vor","delay-in-days":208,"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":["11705077","11775104","11447017"],"award-info":[{"award-number":["11705077","11775104","11447017"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY14A010005"],"award-info":[{"award-number":["LY14A010005"]}],"id":[{"id":"10.13039\/501100004731","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 (3+1)\u2010dimensional Korteweg\u2010de Vries (KdV)\u2010like equation is constructed using the truncated Painlev\u00e9 expansion. Such residual symmetry can be localized and the (3+1)\u2010dimensional KdV\u2010like equation is extended into an enlarged system by introducing some new variables. By using Lie\u2019s first theorem, the finite transformation is obtained for this localized residual symmetry. Further, the linear superposition of multiple residual symmetries is localized and the <jats:italic>n<\/jats:italic>\u2010th B\u00e4cklund transformation in the form of the determinants is constructed for this equation. For illustration more detail, the first three multiple wave solutions\u2010the collisions of resonant solitons are depicted. Finally, with the aid of the link between the consistent tanh expansion (CTE) method and the truncated Painlev\u00e9 expansion, the explicit soliton\u2010cnoidal wave interaction solution containing three kinds of Jacobian elliptic functions for this equation is derived.<\/jats:p>","DOI":"10.1155\/2019\/8034731","type":"journal-article","created":{"date-parts":[[2019,7,28]],"date-time":"2019-07-28T23:31:18Z","timestamp":1564356678000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Resonant Soliton and Soliton\u2010Cnoidal Wave Solutions for a (3+1)\u2010Dimensional Korteweg\u2010de Vries\u2010Like Equation"],"prefix":"10.1155","volume":"2019","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5389-2052","authenticated-orcid":false,"given":"Zheng-Yi","family":"Ma","sequence":"first","affiliation":[]},{"given":"Jin-Xi","family":"Fei","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8911-6031","authenticated-orcid":false,"given":"Jun-Chao","family":"Chen","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6592-7905","authenticated-orcid":false,"given":"Quan-Yong","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2019,7,28]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1364\/OE.20.007469"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.31.000188"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2560-9"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-2941-8"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3027-3"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3399-z"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3725-5"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4868244"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.7498\/aps.67.20180094"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0198-0149(80)90015-1"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112092002374"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.2298\/TSCI160809056D"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1088\/0741-3335\/55\/5\/055005"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.4776710"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/108\/20005"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-015-2406-5"},{"volume-title":"Darboux Transformations in Integrable Systems Theory and Their Applications to Geometry: Mathematical Physics Studies","year":"2005","author":"Gu C.","key":"e_1_2_9_17_2"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/30\/5\/004"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.85.056607"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511606359"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/JHEP05(2013)029"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.523393"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4350-2"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.1002\/sapm1987773253"},{"key":"e_1_2_9_25_2","unstructured":"LouS. 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