{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T12:00:23Z","timestamp":1769601623745,"version":"3.49.0"},"reference-count":20,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,18]],"date-time":"2023-09-18T00:00:00Z","timestamp":1694995200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research","award":["4223"],"award-info":[{"award-number":["4223"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this article, the exact solutions of the stochastic conformable Broer\u2013Kaup equations with conformable derivatives which describe the bidirectional propagation of long waves in shallow water are obtained using the modified exponential function method and the generalized Kudryashov method. These exact solutions consist of hyperbolic, trigonometric, rational trigonometric, rational hyperbolic, and rational function solutions, respectively. This shows that the proposed methods are competent and sufficient. In addition, it is aimed to better understand the physical properties by drawing two- and three-dimensional graphics of the exact solutions according to different parameter values. When these exact solutions obtained by two different methods are compared with the solutions attained by other methods, it can be said that these two methods are competent.<\/jats:p>","DOI":"10.3390\/axioms12090889","type":"journal-article","created":{"date-parts":[[2023,9,19]],"date-time":"2023-09-19T03:02:17Z","timestamp":1695092537000},"page":"889","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Exact Solutions of the Stochastic Conformable Broer\u2013Kaup Equations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0199-6850","authenticated-orcid":false,"given":"Humaira","family":"Yasmin","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yusuf","family":"Pandir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tolga","family":"Akturk","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Science Education, Faculty of Education, Ordu University, 52200 Ordu, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7210-5683","authenticated-orcid":false,"given":"Yusuf","family":"Gurefe","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Mersin University, 33343 Mersin, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,18]]},"reference":[{"key":"ref_1","first-page":"527","article-title":"Comparison of homotopy perturbation method and homotopy analysis method","volume":"156","author":"He","year":"2004","journal-title":"Appl. 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