{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:45:32Z","timestamp":1778021132489,"version":"3.51.4"},"reference-count":49,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T00:00:00Z","timestamp":1728604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we focus on investigating a novel extended (3+1)-dimensional Kadomtsev\u2013Petviashvili\u2013Boussinesq-like (KPB-like) equation. Initially, we utilized the Lie symmetry method to determine the symmetry generator by considering the Lie invariance condition. Subsequently, by similar reduction, the equation becomes ordinary differential equations (ODEs). Exact analytical solutions were derived through the power series method, with a comprehensive proof of solution convergence. Employing the (G\u2032\/G2)-expansion method enabled the identification of trigonometric, exponential, and rational solutions of the equation. Furthermore, we established the auto-B\u00e4cklund transformation of the equation. Multiple-soliton solutions were identified by utilizing Hirota\u2019s bilinear method. The fundamental properties of these solutions were elucidated through graphical representations. Our results are of certain value to the interpretation of nonlinear problems.<\/jats:p>","DOI":"10.3390\/sym16101345","type":"journal-article","created":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T08:10:16Z","timestamp":1728634216000},"page":"1345","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New (3+1)-Dimensional Extension of the Kadomtsev\u2013Petviashvili\u2013Boussinesq-like Equation: Multiple-Soliton Solutions and Other Particular Solutions"],"prefix":"10.3390","volume":"16","author":[{"given":"Xiaojian","family":"Li","sequence":"first","affiliation":[{"name":"School of Science, Jiangnan University, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lianzhong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Science, Jiangnan University, Wuxi 214122, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4064","DOI":"10.1016\/j.cnsns.2012.02.032","article-title":"Lie symmetries and conservation laws of the Hirota\u2013Ramani equation","volume":"17","author":"Nadjafikhah","year":"2012","journal-title":"Commun. 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