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With the help of the Cole\u2014Hopf transform, the Hirota bilinear equation is established, then the symbolic computation with the ansatz function schemes is employed to search for the diverse exact solutions. Some new results such as the multi-wave complexiton, multi-wave, and periodic lump solutions are found. Furthermore, the abundant traveling wave solutions such as the dark wave, bright-dark wave, and singular periodic wave solutions are also constructed by applying the sub-equation method. Finally, the nonlinear dynamic behaviors of the solutions are presented through the 3-D plots, 2-D contours, and 2-D curves and their corresponding physical characteristics are also elaborated. To our knowledge, the obtained solutions in this work are all new, which are not reported elsewhere. The methods applied in this study can be used to investigate the other PDEs arising in physics.<\/jats:p>","DOI":"10.3390\/axioms12010095","type":"journal-article","created":{"date-parts":[[2023,1,17]],"date-time":"2023-01-17T03:41:52Z","timestamp":1673926912000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev\u2014Petviashvili Equation in Fluid Mechanics"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3905-0844","authenticated-orcid":false,"given":"Kang-Jia","family":"Wang","sequence":"first","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing-Hua","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Si","sequence":"additional","affiliation":[{"name":"School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guo-Dong","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":[[2023,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110578","DOI":"10.1016\/j.chaos.2020.110578","article-title":"Quasi-periodic, chaotic and travelling wave structures of modified Gardner equation","volume":"143","author":"Jhangeer","year":"2021","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2350072","DOI":"10.1142\/S021988782350072X","article-title":"New perspective to the fractal Konopelchenko-Dubrovsky equations with M-truncated fractional derivative","volume":"2023","author":"Wang","year":"2023","journal-title":"Int. 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