{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:12:08Z","timestamp":1760148728395,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,5,25]],"date-time":"2023-05-25T00:00:00Z","timestamp":1684972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Programs of Universities in Henan Province of China","award":["22A140006","B2018-40","21IRTSTHN016"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016"]}]},{"name":"Program of Henan Polytechnic University","award":["22A140006","B2018-40","21IRTSTHN016"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016"]}]},{"name":"the Innovative Scientists and Technicians Team of Henan Provincial High Education","award":["22A140006","B2018-40","21IRTSTHN016"],"award-info":[{"award-number":["22A140006","B2018-40","21IRTSTHN016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the present study, two effective methods, the Exp-function method and He\u2019s frequency formulation, are employed to investigate the dynamic behaviors of the (3+1)-dimensional Boiti\u2013Leon\u2013Manna\u2013Pempinelli equation, which is used widely to describe the incompressible fluid. A variety of the wave structures, including the dark wave, bright-dark wave and periodic wave solutions, are successfully constructed. Compared with the results attained by the methods, the obtained solutions are all new and have not been presented in the other literature. The diverse wave structures of the solutions are presented through numerical results in the form of three-dimensional plots and two-dimensional curves. It reveals that the proposed methods are powerful and straightforward, which are expected to be helpful for the study of travelling-wave theory in fluid.<\/jats:p>","DOI":"10.3390\/axioms12060519","type":"journal-article","created":{"date-parts":[[2023,5,26]],"date-time":"2023-05-26T02:05:44Z","timestamp":1685066744000},"page":"519","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the Wave Structures to the (3+1)-Dimensional Boiti\u2013Leon\u2013Manna\u2013Pempinelli Equation in Incompressible Fluid"],"prefix":"10.3390","volume":"12","author":[{"given":"Yan-Nan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-0844","authenticated-orcid":false,"given":"Kang-Jia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"167258","DOI":"10.1016\/j.ijleo.2021.167258","article-title":"Multiple optical soliton solutions for CGL equation with Kerr law nonlinearity via extended modified auxiliary equation mapping method","volume":"242","author":"Akram","year":"2021","journal-title":"Optik"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1140\/epjp\/i2018-12354-9","article-title":"More general families of exact solitary wave solutions of the nonlinear Schr\u00f6dinger equation with their applications in nonlinear optics","volume":"133","author":"Cheemaa","year":"2018","journal-title":"Eur. 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