{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T01:44:29Z","timestamp":1775007869896,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T00:00:00Z","timestamp":1653436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This article demonstrates how the new Double Laplace\u2013Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs.<\/jats:p>","DOI":"10.3390\/axioms11060247","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T08:41:33Z","timestamp":1653468093000},"page":"247","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1324-0823","authenticated-orcid":false,"given":"Shams A.","family":"Ahmed","sequence":"first","affiliation":[{"name":"Department of Mathematic, Faculty of Sciences and Arts, Jouf University, Tubarjal 74756, Saudi Arabia"},{"name":"Department of Mathematic, University of Gezira, Wad Madani 21111, Sudan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8404-3897","authenticated-orcid":false,"given":"Ahmad","family":"Qazza","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zarqa University, Zarqa 13110, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6394-1452","authenticated-orcid":false,"given":"Rania","family":"Saadeh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zarqa University, Zarqa 13110, Jordan"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/0895-7177(90)90125-7","article-title":"A review of the decomposition method and some recent results for nonlinear equations","volume":"13","author":"Adomian","year":"1990","journal-title":"Math. 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