{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T02:41:34Z","timestamp":1780368094247,"version":"3.54.1"},"reference-count":37,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,7,29]],"date-time":"2023-07-29T00:00:00Z","timestamp":1690588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University","award":["PNURSP2023R 273"],"award-info":[{"award-number":["PNURSP2023R 273"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We take into account the (2 + 1)-dimensional stochastic Kadomtsev\u2013Petviashvili equation with beta-derivative (SKPE-BD) in this paper. To develop new hyperbolic, trigonometric, elliptic, and rational solutions, the Riccati equation and Jacobi elliptic function methods are employed. Because the KP equation is required for explaining the development of quasi-one-dimensional shallow-water waves, the solutions obtained can be used to interpret various attractive physical phenomena. To display how the multiplicative white noise and beta-derivative impact the exact solutions of the SKPE-BD, we plot a few graphs in MATLAB and display different 3D and 2D figures. We deduce how multiplicative noise stabilizes the solutions of SKPE-BD at zero.<\/jats:p>","DOI":"10.3390\/axioms12080748","type":"journal-article","created":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T03:30:02Z","timestamp":1690774202000},"page":"748","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Effects of the Wiener Process and Beta Derivative on the Exact Solutions of the Kadomtsev\u2013Petviashvili Equation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2394-0041","authenticated-orcid":false,"given":"Farah M.","family":"Al-Askar","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1694-7907","authenticated-orcid":false,"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II 39, 00186 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1402-7584","authenticated-orcid":false,"given":"Wael W.","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"036126","DOI":"10.1103\/PhysRevE.69.036126","article-title":"Reaction front in an A+B\u2192C reaction\u2013subdiffusion process","volume":"69","author":"Yuste","year":"2004","journal-title":"Phys. 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