{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T10:02:31Z","timestamp":1762077751478,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T00:00:00Z","timestamp":1668988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, we discuss the (2 + 1)-D coupled Korteweg\u2013De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the \u03c7-Wick-type product. White noise functional solutions (WNFS) are presented with the homogeneous equilibrium principle, Hermite transform (HT), and technicality via the F-expansion procedure. By means of the direct connection between the theory of hypercomplex systems (HCS) and white noise analysis (WNA), we establish non-Gaussian white noise (NGWN) by studying stochastic partial differential equations (PDEs) with NG-parameters. So, by using the F-expansion method we present multiples of exact and stochastic families from variable coefficients of travelling wave and stochastic NG-functional solutions of (2 + 1)-D C-KdV equations. These solutions are Jacobi elliptic functions (JEF), trigonometric, and hyperbolic forms, respectively.<\/jats:p>","DOI":"10.3390\/axioms11110658","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T03:13:41Z","timestamp":1669086821000},"page":"658","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Hypercomplex Systems and Non-Gaussian Stochastic Solutions with Some Numerical Simulation of \u03c7-Wick-Type (2 + 1)-D C-KdV Equations"],"prefix":"10.3390","volume":"11","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5063-5301","authenticated-orcid":false,"given":"Mahmoud A.","family":"Abd-Rabo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2222-7973","authenticated-orcid":false,"given":"Ghada","family":"AlNemer","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,21]]},"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. F Math. Decis. Sci."},{"key":"ref_2","unstructured":"Zakarya, M. (2017). Hypercomplex Systems with Some Applications of White Noise Analysis, LAP LAMBERT Academic Publishing. ISBN-13: 978-620-2-07650-0."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s12190-009-0338-2","article-title":"Exact solutions for non-linear Schrodinger equations by differential transformation method","volume":"35","author":"Borhanifar","year":"2011","journal-title":"J. Appl. Math. 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