{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T23:05:18Z","timestamp":1779923118957,"version":"3.53.1"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Basque Government","award":["IT1555-22"],"award-info":[{"award-number":["IT1555-22"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>KdV equations have a lot of applications of in fluid mechanics. The exact solutions of the KdV equations play a vital role in the wave dynamics of fluids. In this paper, some new exact solutions of a generalized geophysical KdV equation are computed with the aid of tanh-coth method. To implement the tanh-coth procedure, we first convert the PDEs to ODEs with the help of wave transformation. Then, using a system of algebraic equations, we obtain several soliton solutions. To verify and clearly illustrate the exact solutions, several graphic presentations are developed by giving the parameter values, which are then thoroughly discussed in the relevant components.<\/jats:p>","DOI":"10.3390\/sym15010135","type":"journal-article","created":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T02:33:21Z","timestamp":1672713201000},"page":"135","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":53,"title":["Periodic, Singular and Dark Solitons of a Generalized Geophysical KdV Equation by Using the Tanh-Coth Method"],"prefix":"10.3390","volume":"15","author":[{"given":"Surapol","family":"Naowarat","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Technology, Suratthani Rajabhat University, Surat Thani 84100, Thailand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sayed","family":"Saifullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5610-6248","authenticated-orcid":false,"given":"Shabir","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9320-9433","authenticated-orcid":false,"given":"Manuel","family":"De la Sen","sequence":"additional","affiliation":[{"name":"Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, Campus of Leioa (Bizkaia), University of the Basque Country, 48940 Leioa, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.joes.2021.09.015","article-title":"Soliton solutions for time fractional ocean engineering models with Beta derivative","volume":"7","author":"Ahmad","year":"2022","journal-title":"J. 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