{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:45Z","timestamp":1760146665725,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,11,24]],"date-time":"2024-11-24T00:00:00Z","timestamp":1732406400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Khalid University","award":["RGP 2\/190\/45"],"award-info":[{"award-number":["RGP 2\/190\/45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we obtain non-Gaussian (NG) stochastic solutions to \u03c7-Wick-type stochastic (\u03c7-Wk-TS) Burgers\u2019 equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems (HCSs), the \u03c7-Wick product (\u03c7-Wk-product) and an \u03c7-Hermite transform (\u03c7-Hr-transform) are proposed. We provide a new set of non-Gaussian solitary wave solutions (NG-SWSs) to Burgers\u2019 equations with variable coefficients. NG white noise functional solutions (NG-WNFSs) to \u03c7-Wk-TS Burgers\u2019 equations with variable coefficients are shown. The symmetry coefficients of partial differential equations and the symmetrical properties of SPDEs are critical in determining the best solution.<\/jats:p>","DOI":"10.3390\/sym16121572","type":"journal-article","created":{"date-parts":[[2024,11,25]],"date-time":"2024-11-25T05:21:32Z","timestamp":1732512092000},"page":"1572","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Travelling Solitary Wave Solutions to Non-Gaussian \u03c7-Wick-Type Stochastic Burgers\u2019 Equation with Variable Coefficients"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4312-8330","authenticated-orcid":false,"given":"Mohammed","family":"Zakarya","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"}]},{"given":"Manal","family":"Al-Qarni","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}]},{"given":"Tahani","family":"Al-Qahtani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,24]]},"reference":[{"key":"ref_1","first-page":"11","article-title":"A construction of non-Gaussian white noise analysis using the theory of hypercomplex systems","volume":"16","author":"Ghany","year":"2016","journal-title":"Glob. J. Sci. Front. Res. Math. Decis. 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