{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:41:18Z","timestamp":1760143278192,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T00:00:00Z","timestamp":1705968000000},"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 paper focuses on obtaining traveling wave solutions of the Fornberg\u2013Whitham model derived from Gilson\u2013Pickering equations, which describe the prorogation of waves in crystal lattice theory and plasma physics by some analytical techniques, i.e., the exp-function method (EFM), the multi-exp function method (MEFM) and the multi hyperbolic tangent method (MHTM). We analyze and compare them to show that MEFM is the optimum method.<\/jats:p>","DOI":"10.3390\/axioms13020074","type":"journal-article","created":{"date-parts":[[2024,1,23]],"date-time":"2024-01-23T07:22:32Z","timestamp":1705994552000},"page":"74","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Solving the Fornberg\u2013Whitham Model Derived from Gilson\u2013Pickering Equations by Analytical Methods"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4096-1469","authenticated-orcid":false,"given":"Donal","family":"O\u2019Regan","sequence":"first","affiliation":[{"name":"School of Mathematical and Statistical Sciences, University of Galway, University Road, H91 TK33 Galway, Ireland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3108-6524","authenticated-orcid":false,"given":"Safoura Rezaei","family":"Aderyani","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6770-6951","authenticated-orcid":false,"given":"Reza","family":"Saadati","sequence":"additional","affiliation":[{"name":"School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6673-3560","authenticated-orcid":false,"given":"Tofigh","family":"Allahviranloo","sequence":"additional","affiliation":[{"name":"Research Center of Performance and Productivity Analysis, Istinye University, 34010 Istanbul, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4318192","DOI":"10.1155\/2022\/4318192","article-title":"The exact solutions of the conformable time-fractional modified nonlinear Schr\u00f6dinger equation by the Trial equation method and modified Trial equation method","volume":"2022","author":"Aderyani","year":"2022","journal-title":"Adv. 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