{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:25:29Z","timestamp":1760059529995,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:00:00Z","timestamp":1750291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Deanship at the University of Ha\u2019il-Saudi Arabia","award":["RG-24097"],"award-info":[{"award-number":["RG-24097"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Here, we consider the stochastic graphene sheets model (SGSM) forced by multiplicative noise in the It\u00f4 sense. We show that the exact solution of the SGSM may be obtained by solving some deterministic counterparts of the graphene sheets model and combining the result with a solution of stochastic ordinary differential equations. By applying the extended tanh function method, we obtain the soliton solutions for the deterministic counterparts of the graphene sheets model. Because graphene sheets are important in many fields, such as electronics, photonics, and energy storage, the solutions of the stochastic graphene sheets model are beneficial for understanding several fascinating scientific phenomena. Using the MATLAB program, we exhibit several 3D graphs that illustrate the impact of multiplicative noise on the exact solutions of the SGSM. By incorporating stochastic elements into the equations that govern the evolution of graphene sheets, researchers can gain insights into how these fluctuations impact the behavior of the material over time.<\/jats:p>","DOI":"10.3390\/axioms14060477","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T09:57:48Z","timestamp":1750327068000},"page":"477","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Abundant Exact Traveling-Wave Solutions for Stochastic Graphene Sheets Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1402-7584","authenticated-orcid":false,"given":"Wael W.","family":"Mohammed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2907-3353","authenticated-orcid":false,"given":"Taher S.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rabeb","family":"Sidaoui","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hijyah","family":"Alshammary","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4005-9595","authenticated-orcid":false,"given":"Mohamed S.","family":"Algolam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"129","DOI":"10.2478\/AMNS.2019.1.00013","article-title":"New complex hyperbolic structures to the lonngren-wave equation by using sine-gordon expansion method","volume":"4","author":"Baskonus","year":"2019","journal-title":"Appl. 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