{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T22:45:29Z","timestamp":1778021129552,"version":"3.51.4"},"reference-count":18,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,22]],"date-time":"2026-02-22T00:00:00Z","timestamp":1771718400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Postgraduate Studies and Scientific Research at Majmaah University","award":["R-2026-63"],"award-info":[{"award-number":["R-2026-63"]}]},{"name":"Deanship of Graduate Studies and Scientific Research at Qassim University","award":["QU-APC-2026"],"award-info":[{"award-number":["QU-APC-2026"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The (3+1)-dimensional B-type Kadomtsev\u2013Petviashvili (BKP) problem was examined in this paper using the developed Exp-function method (DEFM) and Lie symmetry analysis. The objective of this research is studying the BKP equation to get novel exact solutions. Symmetry analysis has been used to determine similarity variables and vector fields. The governing equation was reduced to five variant ordinary differential equations (ODEs). The DEFM was employed for four of them to obtain several novel exact solutions that contain arbitrary constants. The most appropriate choice of values for these optional constants contributed to the emergence of solutions, such as double waves, multisolitons, kink waves, anti-kink waves, and solitary waves. The obtained exact solutions are presented in a 3D graph. The behavior of the solutions can be utilized to explore the application of the governing equation in fluid dynamics, plasma physics, nonlinear optics, and ocean physics.<\/jats:p>","DOI":"10.3390\/axioms15020156","type":"journal-article","created":{"date-parts":[[2026,2,23]],"date-time":"2026-02-23T08:58:21Z","timestamp":1771837101000},"page":"156","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lie Symmetry and Various Exact Solutions for (3+1)-Dimensional B-Type Kadomtsev\u2013Petviashvili Equation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-0948-3207","authenticated-orcid":false,"given":"Ahmed A.","family":"Gaber","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majmaah 15341, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-6947-2905","authenticated-orcid":false,"given":"Dalal","family":"Alhwikem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Burydah 52571, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8325-7500","authenticated-orcid":false,"given":"Abdul-Majid","family":"Wazwaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2025","DOI":"10.1016\/j.camwa.2010.08.060","article-title":"Exp-function method for solving nonlinear evolution equations with higher order nonlinearity","volume":"61","author":"Gurefe","year":"2011","journal-title":"Comput. 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