{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T22:14:03Z","timestamp":1771539243382,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T00:00:00Z","timestamp":1700092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Ha\u2019il-Saudi Arabia","award":["GR-23026"],"award-info":[{"award-number":["GR-23026"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, the stochastic Riemann wave equation (SRWE) forced by white noise in the It\u00f4 sense is considered. The extended tanh function and mapping methods are applied to obtain new elliptic, rational, hyperbolic, and trigonometric stochastic solutions. Furthermore, we generalize some previous studies. The obtained solutions are important in explaining some exciting physical phenomena, since the SRWE is required for describing wave propagation. We plot numerous 3D and 2D graphical representations to explain how the multiplicative white noise influences the exact solutions of the SRWE. We can infer that the introduction of multiplicative white noise disrupts the symmetry of the solutions and serves to stabilize the solutions of the SRWE.<\/jats:p>","DOI":"10.3390\/sym15112070","type":"journal-article","created":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T01:56:29Z","timestamp":1700099789000},"page":"2070","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Impact of White Noise on the Exact Solutions of the Stochastic Riemann Wave Equation in Quantum Mechanics"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1402-7584","authenticated-orcid":false,"given":"Wael","family":"Mohammed","sequence":"first","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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Doaa","family":"Rizk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts in Al-Asyah, Qassim University, Buraidah 6640, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Elkhateeb","family":"Aly","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Jazan University, Jazan 45142, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mahmoud","family":"El-Morshedy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Arnold, L. (1998). Random Dynamical Systems, Springer.","DOI":"10.1007\/978-3-662-12878-7"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1142\/S0219493702000443","article-title":"Conceptual stochastic climate models","volume":"2","author":"Imkeller","year":"2002","journal-title":"Stoch. Dynam."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Mouy, M., Boulares, H., Alshammari, S., Alshammari, M., Laskri, Y., and Mohammed, W.W. (2023). On Averaging Principle for Caputo-Hadamard Fractional Stochastic Differential Pantograph Equation. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7010031"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Mohammed, W.W., Al-Askar, F.M., and Cesarano, C. (2023). Solitary solutions for the stochastic Fokas system found in monomode optical fibers. 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