{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:32:44Z","timestamp":1760059964080,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T00:00:00Z","timestamp":1753228800000},"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 the variable coefficients geophysical KdV (VCGKdV) equation, which involves time-dependent perturbation, nonlinearity and dispersion parameters. It is a more realistic model than its constant coefficient counterpart and can be useful to, for instance, investigate the Coriolis effect on oceanic flows. Firstly, we analyzed this model using three strong methods that allow the investigation of its integrability: the Lie symmetry approach, Painlev\u00e9 property and Hirota formalism. The general constraints between the involved parameters under which the complete integrability in Lie, Painlev\u00e9 or Hirota sense exists, as well as the largest class of this type of equations, which admits the same class of imposed symmetries are generated. Then, some new specific families of solutions for the model endowed with either Lie symmetry properties, Lie and Painlev\u00e9 constraints or with Lie, Painlev\u00e9 and Hirota constraints were generated and compared with solutions derived with other techniques. By numerical simulations, the dynamical behaviors of some Lie invariant solutions and nonautonomous multiple solitons are depicted.<\/jats:p>","DOI":"10.3390\/axioms14080557","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T14:22:44Z","timestamp":1753280564000},"page":"557","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Compatibility of Some Integrability Methods and Related Solutions for the Variable Coefficients Geophysical KdV Model"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8841-4421","authenticated-orcid":false,"given":"Rodica","family":"Cimpoiasu","sequence":"first","affiliation":[{"name":"The Research Center for Applied Life Sciences and Biotechnologies, University of Craiova, 13 A. I. Cuza Street, 200585 Craiova, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4841-5606","authenticated-orcid":false,"given":"Radu","family":"Constantinescu","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Craiova, 13 A. I. Cuza Street, 200585 Craiova, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5130-1343","authenticated-orcid":false,"given":"Corina Nicoleta","family":"Babalic","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Craiova, 13 A. I. Cuza Street, 200585 Craiova, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"796","DOI":"10.1016\/j.jmaa.2018.11.014","article-title":"The inverse scattering transform and soliton solutions of a combined modified Korteweg\u2013de Vries equation","volume":"471","author":"Ma","year":"2019","journal-title":"J. Math. Anal. 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