{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T17:31:16Z","timestamp":1775323876487,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,1]],"date-time":"2025-04-01T00:00:00Z","timestamp":1743465600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12375006"],"award-info":[{"award-number":["12375006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12105243"],"award-info":[{"award-number":["12105243"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LQ22A050002"],"award-info":[{"award-number":["LQ22A050002"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Zhejiang Province of China","award":["12375006"],"award-info":[{"award-number":["12375006"]}]},{"name":"Natural Science Foundation of Zhejiang Province of China","award":["12105243"],"award-info":[{"award-number":["12105243"]}]},{"name":"Natural Science Foundation of Zhejiang Province of China","award":["LQ22A050002"],"award-info":[{"award-number":["LQ22A050002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The generalized (2 + 1)-dimensional Date\u2013Jimbo\u2013Kashiwara\u2013Miwa (gDJKM) equation, which can be used to describe some phenomena in fluid mechanics, is investigated based on the multi-soliton solution. Soliton molecules of the gDJKM equation are given by the velocity resonance mechanism. A soliton molecule containing three solitons is portrayed at different times. The invariance of the relative positions of three solitons confirms that they form a soliton molecule. Multi-order lumps are obtained by applying the long-wave limit method in the multi-soliton. By analyzing the dynamics of one-order and two-order lumps, the energy concentration and localization property for lump waves are displayed. In the meanwhile, a multi-soliton can transform into multi-order breathers by the complex conjugation relations of parameters. The interaction among lumps, breathers and soliton molecules can be constructed by combining the above comprehensive analysis. The interaction between a one-order lump and a soliton molecule is an elastic collision, which can be observed through investigating evolutionary processes. The results obtained in this paper are useful for explaining certain nonlinear phenomena in fluid dynamics.<\/jats:p>","DOI":"10.3390\/sym17040538","type":"journal-article","created":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T05:43:33Z","timestamp":1743572613000},"page":"538","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Soliton Molecules, Multi-Lumps and Hybrid Solutions in Generalized (2 + 1)-Dimensional Date\u2013Jimbo\u2013Kashiwara\u2013Miwa Equation in Fluid Mechanics"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0000-5062-5699","authenticated-orcid":false,"given":"Wei","family":"Zhu","sequence":"first","affiliation":[{"name":"College of Teacher Education, Quzhou University, Quzhou 324000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hai-Fang","family":"Song","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University of Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wan-Li","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University of Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2497-8076","authenticated-orcid":false,"given":"Bo","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University of Technology, Hangzhou 310014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,1]]},"reference":[{"key":"ref_1","first-page":"539","article-title":"On the stability of solitary waves in weakly dispersing media","volume":"15","author":"Kadomtsev","year":"1970","journal-title":"Sov. 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