{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T07:27:00Z","timestamp":1773041220794,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T00:00:00Z","timestamp":1691107200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Researchers Supporting Project","award":["RSPD2023R802"],"award-info":[{"award-number":["RSPD2023R802"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This research work introduces a novel method called the Sumudu\u2013generalized Laplace transform decomposition method (SGLDM) for solving linear and nonlinear non-homogeneous dispersive Korteweg\u2013de Vries (KdV)-type equations. The SGLDM combines the Sumudu\u2013generalized Laplace transform with the Adomian decomposition method, providing a powerful approach to tackle complex equations. To validate the efficacy of the method, several model problems of dispersive KdV-type equations are solved, and the resulting approximate solutions are expressed in series form. The findings demonstrate that the SGLDM is a reliable and robust method for addressing significant physical problems in various applications. Finally, we conclude that this transform is a symmetry to other symmetric transforms.<\/jats:p>","DOI":"10.3390\/sym15081540","type":"journal-article","created":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T09:27:48Z","timestamp":1691141268000},"page":"1540","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Solution of Fractional Third-Order Dispersive Partial Differential Equations and Symmetric KdV via Sumudu\u2013Generalized Laplace Transform Decomposition"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1820-9921","authenticated-orcid":false,"given":"Hassan","family":"Eltayeb","sequence":"first","affiliation":[{"name":"Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9344-2008","authenticated-orcid":false,"given":"Reem K.","family":"Alhefthi","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2019","DOI":"10.1016\/j.aml.2011.05.035","article-title":"Laplace transform and fractional differential equations","volume":"24","author":"Li","year":"2011","journal-title":"Appl. Math. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"422","DOI":"10.1080\/14786449508620739","article-title":"XLI. 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